Federer needed just 16 minutes to win the opening set in a 6-0, 7-5, 6-4 defeat of Mannarino to reach his 16th Wimbledon quarter-final.
Being made to play his fourth round and quarter-final matches on successive days cost Djokovic dear last July as he not only ended up retiring hurt from in his last-eight contest but also had to call time on his 2017 season.
Federer came out firing in the opener and subsequently dismantled Mannarino in a bagel set that lasted just 16 minutes.
The underdog was far more competitive thereafter, but Federer still triumphed easily and will face Gael Monfils or Kevin Anderson in his 16th Wimbledon quarterfinal.
Federer has now won 32 straight sets at Wimbledon, two shy of his career best in 2005-06.
"It was great to win that first set so quickly", Federer told the BBC.
"It was an important victory as since 2011 I have not been in the quarterfinals of Wimbledon". I'm a big player, big serve.
The win also allowed Isner, the highest-ranked US 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.
Nadal hit 37 winners to only 12 unforced errors and erased the only break he allowed by breaking back immediately in 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. And he watched it again and again, taking note of Federer's quickness, net game, serve, variety of tactics and, above all, his composure.
Monday's win took Nadal, 32, into a 35th Grand Slam quarter-final.
Prince Louis' Godparents Compared To Princess Charlotte & Prince George's: The Major Differences
The 36-year-old arrived hand-in-hand with her husband the Duke of Sussex ahead of the service at the Chapel Royal at St. Prince Louis was born on April 23 and is a younger brother to Prince George , 4, and Princess Charlotte , 3.
"If he's in the final, I am excited to play Roger", he said. Only my second time out on Centre Court.
Monfils made the semi-final at the French Open in 2008 and at the US Open in 2016.
World number one Nadal has now reached the last eight in four consecutive Grand Slams for the first time since 2011 but he will not want to stop there.
Anderson, Isner and Nishikori all reached the Wimbledon quarterfinals for the first time.
"I think", Federer said when it was over, "I can be very pleased".
"I mean, I'm definitely going to have to look at it the right way".
Novak Djokovic was kept waiting in the wings till after 7 pm local time before he could start swinging his racket against Russia's Karen Khachanov at Wimbledon on Monday.
All England Club chief executive Richard Lewis, meanwhile, says Wimbledon organisers will not alter the schedule to accommodate a potential England final appearance.
If Federer does win a ninth title the chances are he will be celebrating at the champions' ball on Sunday evening alongside his friend and contemporary Serena Williams, also 36 - and with three majors more than him at 23.
In her third Wimbledon quarterfinal, Cibulkova faces former French Open champion Jelena Ostapenko.
- Gazza's message for Southgate and his England squad
- Prince Louis's christening to take place in the Chapel Royal
- And is now forecasting a Belgium-England final
- WhatsApp begins its hard battle against fake news in India
- France v Belgium: Four key head-to-head battles
- Boris Johnson resigns in government Brexit meltdown
- Air India changes Taiwan to Chinese Taipei
- Apple Enables USB Restricted Mode by Default in iOS 11.4.1
- India thump England to clinch T20 series after Rohit Sharma century
- Serena Williams extends Wimbledon winning run to make quarters