A year after perishing in a shock second-round defeat, the seven-times champion spared his legion of fans another dose of nail-biting drama as he produced a masterclass in serving.
Federer was greeted by a large red banner reading 'King of Court' and he made sure he lived up to the proclamation as he dropped only nine points on serve during a 94-minute demolition job.
The Swiss next faces Spaniard Marcel Granollers or Santiago Giraldo of Colombia.
Australian teenager Nick Kyrgios staged a stunning comeback to beat French 13th seed Richard Gasquet 3-6 6-7(4) 6-4 7-5 10-8 in the second round of Wimbledon on Thursday after surviving nine match points.
Roared on by a vociferous Australian contingent on Court Two, the 19-year-old wildcard showed incredible resilience to complete the biggest win of his career.
Having fended off a succession of match points, one of which was saved after a successful Hawkeye appeal on a second serve, he broke former semi-finalist Gasquet's serve at 8-8 in a deciding set that captivated the crowd for 71 minutes.
Serving for the match, he then showed no nerves as he held to love, sealing victory with his 21st ace and flinging his racket to the court in apparent disbelief.
The highly-rated Kyrgios, one of a batch of young Australians hoping to revive the fortunes of the former powerhouse nation, was serenaded by the yellow-clad Aussie fans.
Kyrgios was one of five Australians to reach the second round of the men's singles - the most since 1999 - and will fancy his chances of further progress when he meets unseeded Czech youngster Jiri Vesely in the next round.
Jo-Wilfried Tsonga just cannot keep off the grass at Wimbledon this year, having played on all four days of the championships so far during a torturous route to the third round.
The popular Frenchman, twice a semi-finalist at the All England Club, needed two days and five sets to beat Austrian Jurgen Melzer in round one and came through another two-part thriller against American Sam Querrey on Thursday.
There will be no rest for the 14th seed on Friday either because he will be required to sign in for action against Taiwan's Jimmy Wang, the world No.147.
"Of course it's not like I played only three sets," said Tsonga, who was tied at 9-9 in the fifth set against Querrey when darkness fell on Wednesday, returning on Thursday to complete a 4-6 7-6(2) 6-7(4) 6-3 14-12 victory.
"But, you know, I'm feeling okay. I'm ready for that, ready to fight. I hope tomorrow is going to be a good day for me again."
Results from the Wimbledon Men's Singles Round 2 matches on Thursday
4-Roger Federer (Switzerland) beat Gilles Muller (Luxembourg) 6-3 7-5 6-3
9-John Isner (US) beat Jarkko Nieminen (Finland) 7-6(17) 7-6(3) 7-5
Denis Istomin (Uzbekistan) beat Julian Reister (Germany) 7-6(7) 6-4 6-4
5-Stanislas Wawrinka (Switzerland) beat Lu Yen-Hsun (Taiwan) 7-6(6) 6-3 3-6 7-5
14-Jo-Wilfried Tsonga (France) beat Sam Querrey (U.S.) 4-6 7-6(2) 6-7(4) 6-3 14-12
23-Tommy Robredo (Spain) beat Adrian Mannarino (France) 6-4 6-1 7-6(5)
2-Rafa Nadal (Spain) beat Lukas Rosol (Czech Republic) 4-6 7-6(6) 6-4 6-4
Nick Kyrgios (Australia) beat 13-Richard Gasquet (France) 3-6 6-7(4) 6-4 7-5 10-8
Jiri Vesely (Czech Republic) beat 24-Gael Monfils (France) 7-6(3) 6-3 6-7(1) 6-7(3) 6-4
Lukasz Kubot (Poland) beat Dusan Lajovic (Serbia) 6-7(4) 7-6(4) 6-3 7-6(3)
Simone Bolelli (Italy) beat 22-Philipp Kohlschreiber (Germany) 4-6 6-4 6-3 2-6 7-5
8-Milos Raonic (Canada) beat Jack Sock (US) 6-3 6-4 6-4
Mikhail Kukushkin (Kazakhstan) beat Frank Dancevic (Canada) 6-3 6-3 6-2
10-Kei Nishikori (Japan) beat Denis Kudla (US) 6-3 6-2 6-1
- Sports & Recreation
- Richard Gasquet
- Nick Kyrgios