Federer will be playing in his 53rd Grand Slam last-eight.
Mannarino won only two points in the first five games and the opening set was brought to an end inside just 16 minutes.
Federer was followed by Serena Williams, she of the seven Wimbledon trophies among her 23 majors, who was hardly challenged in a 6-2, 6-2 win against 120th-ranked qualifier Evgeniya Rodina of Russian Federation.
"It was great to win that first set so quickly", Federer told the BBC.
Williams is 6-2 in her career against Kerber, but the match might be better than expected given the tight major finals played between the two in 2016.
In many respects, the Swiss was playing against a standard he has set for himself on grass, which has become his natural habitat.
The win also allowed Isner, the highest-ranked USA man, to have something about Wimbledon to relish other than his victory in the longest match in tennis history: 70-68 in the fifth set against Nicolas Mahut after 11 hours spread over three days in 2010.
Federer was forced to save three break points in the eighth game of the third set.
Mannarino was nevertheless able to frustrate his illustrious rival in the third set, even threatening to break for a 5-3 lead.
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Thirteen Wimbledon championships between them and 49 grand slam titles overall, it was quite the historic training run.
"I am not saying I am not excited to play against Roger in the final", he said. His problem has always been the first week of Wimbledon, not the second week.
Monfils made the semi-final at the French Open in 2008 and at the US Open in 2016.
"I feel like a lot of aspects of my game can give him a lot of trouble", said Anderson, the first South African man in the Wimbledon quarter-finals since Wayne Ferreira in 1994.
Nadal, a two-time Wimbledon champion, reached his first Wimbledon quarterfinals since 2011, when he was runner-up to Novak Djokovic in 2011.
"I honestly think that I'm going to win one".
He beat Frenchman Gael Monfils for the first time in six attempts and in doing so reached the Wimbledon quarter-finals for the first time - at the 10th attempt.
Camila Giorgi, who has beaten eight top 10 players during her career, is into her first Slam quarter-final, while Dominika Cibulkova reached the Australian Open final in 2014. He next faces No. 13 Milos Raonic, who defeated Mackenzie McDonald of the USA 6-3, 6-4, 6-7 (5), 6-2. No. 14 Daria Kasatkina, 2017 French Open champion Jelena Ostapenko vs. Dominika Cibulkova, and No. 13 Julia Goerges vs.
'I'm looking forward to it and I'm definitely confident that I can keep going'.
All England Club chief executive Richard Lewis, meanwhile, says Wimbledon organisers will not alter the schedule to accommodate a potential England final appearance.