Federer, 39, was pushed to the limit in his first match back on Wednesday when he beat Briton Dan Evans in three sets but the Swiss looked well in control in the opening set against the unseeded Basilashvili.
World No. 1 Jannik Sinner stayed cool to reach the second round of Wimbledon while several of his fellow seeds including Italian compatriot Lorenzo Musetti crashed and burned on a sizzling Tuesday.
Nikoloz Basilashvili has denied allegations that he attacked Neka Dorokashvili in front of their five-year-old son and he has been released on 100,000 lari ($26,000) bail.
Indian qualifier Prajnesh Gunneswaran achieved the biggest win of his career when he stunningly knocked out World No 18 Nikoloz Basilashvili at the Indian Wells ATP Masters event, continuing his dream run.
Sumit Nagal won the Heilbronner Neckarcup ATP Challenger event beating Alexander Ritschard of Switzerland
Stan Wawrinka pulled off a stunning upset on Thursday, beating top-seeded Daniil Medvedev 6-4, 6-7 (7), 6-3 to reach the quarter-finals of the Moselle Open in Metz, France.
The Indo-Croat combination took just an hour and one minute to dispose off their rivals 6-4, 6-2 in their tournament opener.
Prajnesh Gunneswaran announces retirement from professional tennis
Roger Federer will kickstart his claycourt campaign at next month's Geneva Open as he steps up his preparations for the French Open.
Things to watch out for on Day Six of the French Open on Friday:
Home favourite Jo-Wilfried Tsonga sauntered into the semi-finals of the Lyon Open with a 6-0, 6-4 victory over Russian youngster Karen Khachanov on Thursday.
13 of the men's seeds fell at the first hurdle -- a Wimbledon record since 32 seeds were introduced in 2001.
Alexander Zverev cruised past Frenchman Lucas Pouille in straight sets in the first round of the Australian Open on Sunday.
The Swiss star underwent arthroscopic right knee surgeries in February 2020 and May 2020. Federer has played five tournaments since having those surgeries, all of which came this season.
Clearly Nikoloz Basilashvili had come to face Rafael Nadal with a plan but, like Mike Tyson said, everybody has a plan until they're punched in the face.
Novak Djokovic has formally withdrawn from the draw for the Indian Wells tournament, organisers said on Sunday in an indication that the world number one's application for a COVID-19 vaccine waiver to enter the US might have failed.
Rafael Nadal overcame a temporary blip on his way to victory at the ATP Cup on Saturday
Paes and Raja dispatched the pair of Nikoloz Basilashvili and Andreas Haider-Maurer 6-2, 6-3 in their opening round.
Norrie's semi-final opponent will be another American, fourth-seeded Tommy Paul, who crushed Stefan Kozlov 6-3, 6-1 in an all-US matchup.
Australian Nick Kyrgios was expelled from the tournament after going wild in the third set of his match against Casper Ruud.
Serena Williams returns to the Arthur Ashe Stadium on Sunday
Top tweets from the second day's play at the French Open featuring John Peers, Novak Djokovic, Caroline Wozniacki and Kristina Mladenovic:
Mischa Zverev took some of the limelight back from younger brother Alexander when he beat second seed Kei Nishikori to reach the Geneva Open final on Friday.
Novak Djokovic suffered his first defeat of the new season in the Qatar Open semi-finals on Friday, losing in three sets to Spain's Roberto Bautista Agut.
In his pre-tournament news conference in Toronto on Sunday, Nadal said a recurring foot issue he has been dealing with since 2005 returned at the French Open, where he fell to eventual champion Djokovic in the semi-finals.
Photos from Day 1 of the Australian Open matches played at Melbourne Park on Monday
Paula Badosa survived a stiff challenge from Victoria Azarenka in the Indian Wells final, while Cameron Norrie battled back to defeat Nikoloz Basilashvili.
Prajnesh Gunneswaran's terrific run at the Indian Wells Masters came to an end following a straight set defeat against big-serving Ivo Karlovic.
Eight-time Wimbledon champion Roger Federer, who turns 40 this year, takes on Frenchman Adrian Mannarino in round one.
Garbine Muguruza was relieved to finally avoid tripping at the last hurdle and end her trophy drought
Spain and Real Madrid captain Sergio Ramos faced a new setback in a season littered with injury problems when his club said on Tuesday he had tested positive for COVID-19.
Andy Murray returned to the All England Club in the men's doubles on Thursday and eased into the second round with French partner Pierre-Hugues Herbert.
Summary of sports events and persons who made news on Sunday
Wimbledon was invaded by thousands of flying ants on Wednesday, causing much annoyance to players, officials and ticket holders alike - but there was little anyone could do to drive out the pests.
Rafael Nadal saw off Rogerio Dutra Silva 6-1, 6-2 on Wednesday to reach the last 16 of the Barcelona Open, while Andy Murray advanced after opponent Bernard Tomic withdrew.
'I have so much to look forward to in 2021, including the Olympics'
Images from matches played on Day 5 at the Australian Open in Melbourne Park on Friday
Will it be Rafa versus Djoko in Sunday's final?
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