Needing a three-way share of second place to regain the top spot he first earned in September, it left him in sole possession of the runner-up spot at that stage after Finau made a double bogey at the 14th.
But the American picked up two shots in the closing four holes to ensure that compatriot Brooks Koepka, who was not playing this week, remained at the top of the rankings as Rose finished third.
Big-hitting Rahm, the first Spaniard to play in the 20-year history of the event, moved ahead after four birdies in his opening nine holes in Albany.
The 24-year-old world number eight, part of Europe’s triumphant Ryder Cup team in September, wrapped up his third individual title of the year, the sixth of his burgeoning career.
-13 T Finau (US), H Stenson (Swe), J Rahm (Spa); -11 G Woodland (US); -10 R Fowler (US); -9 X Schauffele (US), D Johnson (US); -8 P Reed (US), J Rose (Eng), A Noren (Swe); -6 J Thomas (US)
-5 B Watson (US), P Cantlay (US); -4 B DeChambeau (US), K Bradley (US); -3 J Day (Aus), H Matsuyama (Jpn); -2 T Woods (US)
American Tony Finau, Spaniard Jon Rahm and Henrik Stenson of Sweden share the lead on 13 under after day three of the Hero World Challenge in the Bahamas.
Finau, who shot six birdies in a five-under 67, had the best round of a group who are two clear of Gary Woodland.
Englishman Justin Rose, requiring a top-three finish to return to world number one, is in a three-way share of eighth, five strokes back, after a 68.
Tournament host Tiger Woods is bottom of the 18-man field, 11 off the lead.
Woods dropped three shots in the first three holes but also had five birdies in his 72.
Big-hitting Rahm, the world number eight, who led overnight with Stenson, was eight feet from the pin in two at the 547-yard par five 15th but his eagle putt spun out of the hole.
His birdie effort from the fringe grass at the last suffered the same fate as he finished with a round of 69.
Rose had four birdies in the final seven holes, pitching to three feet at the 17th.
Sweden’s Alex Noren went even closer at the 181-yard par-three, holing his nine-iron tee shot.
The ball pitched a foot short of the flag and it trickled into the cup, completing a remarkable run of eagle, triple bogey, ace in three holes for the world number 18, who is level with Rose at eight under.
World number three Dustin Johnson dropped four strokes in the first two holes, with a triple bogey at the par-three second after two successive shots rolled back down the slope to his feet.
He responded with four birdies in seven holes but finished with a 72 to sit on nine under.
-10 J Rahm (Spa), H Stenson (Swe); -9 D Johnson (USA), P Cantlay (USA); -8 T Finau (USA); -6 G Woodland (USA), A Noren (Swe); -5 R Fowler (USA)
-4 K Bradley (USA), J Rose (Eng), J Thomas (USA); -3 X Schauffele (USA), B DeChambeau (USA); -2 T Woods (USA), H Matsuyama (Jpn), B Watson (USA), P Reed (USA); -1 J Day (Aus)
Spaniard Jon Rahm fired a nine-under 63 to share the halfway lead at the Hero World Challenge in the Bahamas.
The 24-year-old world number eight was joined at 10 under by Sweden’s Henrik Stenson, who posted a 66.
Englishman Justin Rose, seeking a top-three finish to return to world number one, had seven birdies in a 70 and is six shots off the lead.
Tournament host Tiger Woods avoided penalty after a controversial scoop out of a bush and finished two under.
Woods was five under for his round when his tee shot at the last finished under a palmetto bush and he attempted an escape while kneeling in the sand.
Replays showed the ball stayed on the clubface during the shot, but after lengthy discussions, rules officials decided against giving a penalty.
“I didn’t feel like I violated any rules,” said Woods, who finished up with a double bogey. “I was trying to play a shot but the rules committee said they may have been a violation. I didn’t feel like I hit it twice but under super slow-mo you could see I made contact twice.”
The PGA Tour’s vice president of rules and competitions, Mark Russell, said: “We had to look at high-speed, slow-motion video to determine that the ball probably did stay on the clubface a little too long. But there was no way he could’ve known that.”
Explaining the rules under, Russell added: “Basically, if the player didn’t know he did that [hit it twice] and the only way you can tell is by using this type of slow-motion technology, he’s exempt from the rules, so there’s no penalty there.”
From 1 January players will not be penalised for an accidental double-hit.
There is no cut in the elite 18-man field, which features 14 of the world’s top 20 and nine major winners.
One of those, world number three Dustin Johnson, is only one off the lead after five birdies in six holes on the back nine in a round of 67.
-7 P Cantlay (US), P Reed (US); -4 H Stenson (Swe), D Johnson (US); -3 A Noren (Swe), B Watson (US); -2 J Rose (Eng), J Thomas (US), B DeChambeau (US); -1 K Bradley (US), J Rahm (Spa), J Day (Aus)
Level T Finau (US), G Woodland (US), R Fowler (US); +1 T Woods (US), X Schauffele (US); +2 H Matsuyama (Jpn)
Patrick Cantlay and Patrick Reed lead the Hero World Challenge by three shots after seven-under 65s, as tournament host Tiger Woods opened with a 73.
Cantlay birdied five of the last six holes in the Bahamas, while fellow American Reed recorded eight birdies.
Englishman Justin Rose, needing a top-three finish to return to world number one, is five back after a mixed 70.
Woods can regain a place in the top 10 with victory this week and had four birdies, but also a triple bogey.
The American, who was 1,199 in the world rankings during this tournament a year ago, won his first tournament for five years in September with a two-shot victory at the Tour Championship.
Playing in his first event since failing to win a point at the Ryder Cup, he was level par playing the par-three 12th when his chip from the rough on the left rolled back down the slope past his feet and trickled into the water, resulting in a six.
With top-ranked Brooks Koepka not playing this week, world number two Rose played a majestic wood to two feet to eagle the 11th and reach three under but also had problems at the 12th, where he made a double bogey.
Masters champion Reed joined Cantlay at the top of the leaderboard after pitching to three feet to birdie the 16th and then added another with a curling 12-foot effort at the last.
The 18-man field at the Albany course features 14 of the world’s top 20, with five former world number ones and nine major champions.
When England’s Aaron Rai won his first European Tour title at the Hong Kong Open last Sunday, something marked him out as a bit different.
The 24-year-old, who wanted to be an F1 driver before becoming a golfer, is one of a growing number of players of Indian descent making their mark on the game.
But Rai’s difference comes in the form of his kit; the Wolverhampton-born player always wears two gloves come rain or shine, making him look more like a goalkeeper than a golfer.
“I started wearing them from the age of eight for better grip. My game isn’t pretty without them,” he tells BBC Sport.
He is also not your average young millionaire sportsman, either. He is not on social media and he does not have an agent, all a process “to keep things simple,” he says.
It appears to be paying off so far.
Channelling his inner Schumacher
There is some great BBC archive footage of a five-year Rai in action at his local course after winning his first tournament.
The interviewer asks him what he wants to be when he grows up, to which a cheeky-faced Rai replies: “A racing driver”, before bursting into laughter.
Speaking now, he says: “That changed pretty quickly. I used to love watching [seven-time Formula 1 champion] Michael Schumacher back in the day, and it ran so deep that in junior golf competitions I wore Ferrari T-shirts and jumpers.
“That was my thing even from a young age. But since eight or nine, it became very quickly just about golf.”
A putting green was installed in the family’s back garden and by the age of 15, Rai was setting records. After being given a Lee Westwood putting aid, he completed 207 consecutive 10-foot putts.
“I had a couple of attempts which weren’t good but at a third attempt, that happened,” he says. “It was about an hour and a half and afterwards I had a sore back.”
How mum helped him take up golf by accident
The fact Rai took up golf at all was an accident.
After playing with his older brother’s hockey sticks as a toddler, he ended up with a nasty bruise on his head, so his mum went out to buy some plastic sticks to make things a bit safer in the living room.
But she returned home with plastic golf clubs and Rai got to repay his mum in poignant style in 2017.
Dalvir, who is of Kenyan-Indian descent and grew up in Mombasa, decided to escort Aaron to the Kenya Open in Nairobi. It was the first time she had visited the country in 47 years.
So when her son held on to win his first professional tournament on Mother’s Day, it completed a perfect story as she ran on to the 18th green to congratulate him.
“To be able to share that with her was very special,” Rai says. “Those sorts of things don’t happen too often in life so it was amazing.”
His dad is not a ‘pushy parent’
Rai, who made his major debut at the 2017 US Open, says pursuing a career in golf might not always have been met with encouragement from some parents of Indian descent.
But he says his folks have always encouraged him and his dad Amrik has “always been there for support and guidance, but not in a pushy way”.
Amrik was offered a tennis scholarship in the United States at the age of 20, but rejected it.
“Being from an Indian family was different back in those days,” Rai says.
“It was more about getting an education and a proper job, and sport or tennis at that time was never really seen as a proper job.
“That pressure to have certain kinds of career was probably there from the previous generation and certain career paths in our culture are still more walked upon. It’s aspirational to become a lawyer or doctor or dentist and have that kind of status within the family, but it’s beginning to change.
“Sport is a lot bigger than what it was 30 or 40 years ago and when I mean bigger I probably mean in a financial sense.
“It becomes a bit more acceptable to pursue sport as a viable career. You are starting to see some really good Asians come through in certain sports now. Little by little it’s changing and I’m sure it will continue to change in the future.”
Golf ‘becoming more inclusive’
Rai says traditional values could be a reason why there are relatively few Indian golfers on Tour, but he also admits there have been some rare cases of him being subjected to racism, which may also be a factor.
But he says the rise of golfers of Indian descent across the globe is another sign that “the perception of golf is changing” and becoming “a lot more acceptable and more inclusive”.
He cites 22-year-old Indian golfer Shubhankar Sharma, who won twice on the European Tour last season, as “an amazing player, a great symbol for India and already a superstar”.
“Then you’ve got Julian Suri from America who also has Indian origins from his father’s side and Jack Singh Brar, who is British Asian and has just had a incredible year on the Challenge Tour. He will have a great career ahead of him.
“A lot of guys on the Asian tour who have Indian origin who have been very successful. So it is beginning to change and you are seeing more Indians and British Asians getting into golf and performing very well. It’s great to see more and more guys out on Tour now.”
After winning three times on the Challenge Tour and now topping the Race to Dubai rankings after his success in Hong Kong, Rai is sure to be among them.
But he is the only one who will be wearing gloves, even in the searing heat.
Aaron Rai held off fellow Englishman Matthew Fitzpatrick to win his first European Tour title by one shot in the season-opening Hong Kong Open.
Fitzpatrick, 24, chopped Rai’s six-shot overnight lead to one but bogeyed the 17th, allowing the 23-year-old to win on 17 under with a bogey at the last.
“It’s incredible to win on any Tour, let alone The European Tour,” said three-time Challenge Tour winner Rai.
“Matt played incredibly well but I just tried to play the course.”
Fitzpatrick birdied his first two holes to close within four and was three adrift after nine holes. Four more birdies in his next six holes narrowed the gap to one but he missed a four-foot par putt on the penultimate hole to hand the advantage back to Rai.
“It was disappointing on the 17th, such a simple bogey,” said Fitzpatrick, who finished with a six-under 64. “But I gave it a good go.”
England’s Tommy Fleetwood, who started the final round alongside Fitzpatrick in second, dropped back with a three-over 73, one ahead of Scotland’s David Drysdale who carded a 66 to finish fifth.
Sergio Garcia shot a level-par 70 to finish joint sixth with fellow Spaniard Rafa Cabrera Bello and India’s Shubhankar Sharma on nine under par.
Belgium won the World Cup of Golf for the first time with Thomas Pieters and Thomas Detry holding off Mexico and hosts Australia in Melbourne.
The pair went into the final day with a five-shot lead and carded a four-under 68 in Sunday’s alternate shot foursomes to win by three strokes on 23 under.
“It’s been a long time since I won and this feels as good as an individual title. I’m very happy,” said Pieters.
Tyrrell Hatton and Ian Poulter’s 70 left the Englishmen eighth on 15 under.
Ireland’s Shane Lowry and Paul Dunne finished joint 10th on 12 under, while Scottish pair Russell Knox and Martin Laird ended joint 14th on 10 under.
Australia, backed by a vociferous home crowd, started six shots adrift of the Belgians but had four birdies on the front nine and three more from the 12th on the back nine, including Cameron Smith holing a bunker shot on the 14th, lifted them to 20 under par.
Belgium bogeyed the 15th to see their lead cut to two but Australia’s charge stalled when Marc Leishman missed a four-foot birdie putt on the 16th and they finished with two more pars to sign for a 65.
Mexico’s Abraham Ancer, who won last week’s Australian Open, was playing with Roberto Diaz and although the pair did not threaten the lead, three late birdies saw them close with a six-under 66 to join Australia in second.
Defending champions Denmark were tied for fourth at 17 under par alongside Canada.