Federer, who has won 20 Grand Slam titles, was playing for the first time since losing to Australia’s Thanasi Kokkinakis in the second round of the Miami Open on 24 March.
The Swiss, who had a bye in the first round, made a poor start against German Zverev, 30, losing his first set on grass since a defeat by Tommy Haas in this competition last year.
But the reigning Wimbledon champion took the second set and broke Zverev’s serve twice in the deciding set to move into the quarter-finals.
This is only the fifth tournament Federer has played this season. He won the Australian Open in January, the ABN Amro World Tennis Tournament in Rotterdam in February and reached the final of Indian Wells in March.
Federer has won Wimbledon eight times and this year’s tournament starts on 2 July.
India’s Gunneswaran, ranked 169th in the world, caused an upset on Wednesday with a 7-6 (8-6) 2-6 6-3 victory over sixth seed Denis Shapovalov of Canada, the world number 23.
Britain’s first national tennis academies will open in Stirling and Loughborough in 2019 in a bid to boost the number of players in the top 100.
The Lawn Tennis Association (LTA) is setting up the centres as the first major step in its 10-year project to improve British tennis.
Tim Henman and Sam Smith will join an LTA advisory group as part of the plan.
The former British number ones, plus Andy Murray’s coach Jamie Delgado, will advise on performance and strategy.
Britain has four players in the WTA and ATP top 100, with Kyle Edmund ranked highest at 18.
Under the programme, up to 32 players – aged between 11 and 18 – will be selected for a full-time residential programme, which promises a mainstream education at a cost of £5,000 per year.
There will also be 11 regional development centres aimed at improving 10-14-year-olds.
“The new performance strategy has been designed to help create future British tennis champions, who we hope will continue to inspire others to play, watch and enjoy the sport for generations to come,” said LTA chief executive Scott Lloyd.
Russell Fuller, BBC tennis correspondent
The new national academies will be aimed primarily at those between the ages of 13 and 18, but could accommodate children as young as 11 if they meet the criteria.
There will be regional and local centres as well, but the LTA will be investing in fewer venues and individuals as part of its new performance strategy. There will be a maximum of 32 players across the two academies, so the talent identification programme will be crucial.
Costs will, however, be much reduced for the parents of those who do make the grade. The charge will be just £5,000 per year, which includes the expense of weeks on the road at tournaments.
The LTA admits its development programme has suffered from too much chopping and changing in recent years, and the volume of potential top-100 players in the pipeline is not nearly as great as it should be.
The LTA’s ambition, though, is that in 10 years’ time Britain will be one of the most respected nations in the world for player development.
Italy’s Sara Errani says she is disgusted her ban has been increased from two to 10 months after a cancer drug showed up in a failed test.
The former world number five and 2012 French Open runner-up tested positive for banned drug letrozole.
The Court of Arbitration for Sport accepted medication taken by her mother found its way into a family meal.
But it said Errani, 31, was guilty of a “light degree of fault” which justified a 10-month ban.
She reacted by saying: “I am really disgusted by this matter. I don’t think anything similar has ever happened or been managed – in my humble opinion – in such a shameful manner.”
The decision followed appeals by the Italian anti-doping agency, which asked for a longer ban, and Errani, who wanted her voided results to be reinstated.
Errani, who reached the final four of last week’s Croatia Bol Open but withdrew before her semi-final match, must now serve another eight months of suspension.
The winner of five Grand Slam doubles titles was initially banned for two months by the International Tennis Federation (ITF) in August 2017. Her results from 16 February to 7 June that year were declared void.
Errani said her mother had been using the drug as part of her breast cancer treatment and had dropped some pills on a kitchen worktop where tortellini and broth were later prepared.
Letrozole increases lean body mass and was banned by the World Anti-Doping Agency (Wada) over concerns it was being abused by bodybuilders.
An independent tribunal, appointed by the ITF, said there was no evidence it would enhance the performance of an elite tennis player.
‘A very unfair treatment’
Errani’s mother and father told a tribunal hearing in July 2017 that after the positive finding, they carried out an experiment which found the drug dissolved in a broth, plus a meat mixture for tortellini, without being detectable.
“I never took any performance-enhancing substance in all my life, I love tennis too much to do something like that,” said Errani.
“I find this a very unfair treatment and I want to shout it, holding my head up high, because I am sure I have nothing to reproach myself about.”
In 2012 Errani stopped working with Luis Garcia del Moral, one of the doctors at the centre of cyclist Lance Armstrong’s doping scandal.
“I’m not interested in keeping working with a person that is involved in these things,” she said at the time.
He pulled out of planned appearances in Acapulco, Indian Wells and Miami before returning at the start of April for Spain’s Davis Cup tie against Germany.
It was his only appearance before winning the Masters title in Monte Carlo in April, backing that up with victory at the Barcelona Open and another Masters title in Rome.
“I had a lot of months with injury problems, so coming back to win is very special,” he said.
“I came back from five months without playing a full tournament.
“So coming back and having the chance to win in Monte Carlo, Barcelona, Rome, and now especially here, it’s very emotional for me.
“I arrived so-so, with some doubts about this clay-court season.”
Thiem optimistic of final return
Thiem says he is “confident” his first appearance in a Grand Slam final will not be his last.
The 24-year-old finally reached the Roland Garros showpiece after losing in the semi-finals in 2016 and 2017.
“That’s my biggest goal, to get into the next one and then to do it better than today,” he said.
“Of course it’s going to be easier, a little bit, because it’s not going to be the first time anymore.”
Thiem is the only player to have beaten Nadal on clay in the past two years – winning in best-of-three set matches in Rome and Madrid.
However, he fell to a third successive straight-set defeat by the Spaniard at the French Open.
Thiem lost to Nadal in the second round on his Roland Garros debut in 2014, then again in last year’s semi-finals.
“I think it was the first time against him here in Roland Garros where it was a fight,” said Thiem, who told Nadal he remembered being 11 years old and watching the Spaniard win his first title in 2005.
“Honestly, I never expected that one day I would play the finals here so I am still really happy.
“Winning 11 times is definitely one of the best things somebody ever achieved in sport.”
How social media reacted to Nadal’s victory
American 12-time Grand Slam singles champion Billie Jean King: Incredible! Congratulations, Rafael Nadal #champion
German six-time Grand Slam winner Boris Becker: The legend continues… Rafael Nadal @rolandgarros #11
American seven-time French Open winner Chris Evert: Two warriors won at Roland Garros this year… fighters, grinders, with heart and passion…congratulations Simona Halep and Rafael Nadal
American former player Pam Shriver: Bingo legs eleven Rafael Nadal. Chasing RF!
Ex-Real Madrid and Portugal footballer Luis Figo: Congratulations!! Enhorabuena 11x winner Roland Garros. Amazing!!! One of the best sportsman of all times.
Spanish golfer and 2017 Masters champion Sergio Garcia: 11 @rolandgarros for Rafael Nadal!!! Amazing!! What a machine!! Enorme Rafa!!
Coverage: Daily live radio and text commentaries on BBC Radio 5 live, the BBC Sport website and app.
World number one Rafael Nadal won an 11th French Open title by beating Austria’s Dominic Thiem in straight sets.
Nadal, 32, won 6-4 6-3 6-2 to earn his 17th Grand Slam, three adrift of Roger Federer’s all-time men’s record.
The Spaniard edged an intense opening set, tightening his grip in the second.
And he increased the tempo further, consigning Thiem to defeat in his first major final when the Austrian sent a return long.
Nadal is the only second player in history to win the same Grand Slam on 11 occasions after Margaret Court, who won 11 Australian Open titles between 1960 and 1973.
However, it was not all smooth for Nadal, who missed four match points on his own serve before clinching victory when Thiem went long on the fifth.
Nadal dropped his racquet at the baseline in celebration before turning to his box and raising both hands skywards.
The Spaniard had been the hot favourite to win the second Slam of the year, after warming up with three clay-court titles in Monte Carlo, Barcelona and Rome.
The Majorcan has an air of invincibility at Roland Garros, losing only twice in 87 matches since making his debut in 2005, and again he delivered on his favourite stage.
He had breezed through his opening four matches without dropping a set – extending his own personal best to 37 consecutive sets here – though falling short of Bjorn Borg’s all-time record of 41 by losing the opener of his quarter-final against Diego Schwartzman.
That was about as disheartening as it got for the world number one.
Against seventh seed Thiem he was at his destructive best, using his athleticism and mental resilience to wear the Austrian down with his relentless shot-making.
Thiem, playing in his first Grand Slam final, simply had few answers to Nadal’s brilliance.