Federer was in blinding form during the first set, which blazed by in 16 minutes, but after the Swiss missed four break points in the opening game of the second set, Mannarino made more of a match of it.
He has also lost all four meetings against the 20-time major victor, failing to win a set off the great Swiss star.
"I'm very pleased to be back in the second week".
He has fully-justified his seeding of eight and was mentally rock-solid in winning three tiebreaks against Monfils in his four-set win on Court One.
"I wouldn't know that it happened in '05 and '06, I feel like these streaks just happen", Federer said after the match.
"You can't plan for them anyway". "It is part of what a tennis match is about".
Victory for Nadal over his fellow left-hander would take him into a 35th Grand Slam quarterfinal.
And all on a surgically-repaired knee.
"I told my team the other day that for me also, after all these years, it is surprising to be the number one seed, in the top-two rankings at 36", he said. I'm not saying that should happen again.
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"The overall goal is try to win the tournament", the great Spaniard said."These are the matches we work so hard for, me and my whole team". Is true has been a while since I have been in that position.
"At the same time, I have been in that position a couple of times in my career". "I've played Gael a few (five) times and this is the first time I've beaten him". That, of course, is a positive result.
Next up for Nadal is either Juan Martin del Potro, the fifth seeded Argentine, or unseeded Gilles Simon of France.
Just when the third set appeared to be heading to another tiebreak, Monfils took his first break point opportunity at 40-30 up on the Anderson serve, to claim the set 7-5.
If he beats Milos Raonic, seeded 13, he would play either his compatriot John Isner - 10 years older than him but still hungry for success - or the youngest player left in the draw, the 19-year-old rising Greek star Stefanos Tstitsipas.
The world No. 1 faces Czech world No. 93 Jiri Vesely, who has never got past the 4th round of a Grand Slam.
The victor of that clash will take on Kei Nishikori, who overcame a right arm injury to reach his first Wimbledon quarter-final with a gritty 4-6, 7-6 (7/5), 7-6 (12/10), 6-1 win over Latvian qualifier Ernests Gulbis.
Three-time champion Novak Djokovic, seeded a lowly 12 this year, can make his 10th Wimbledon quarter-final if he defeats unseeded Karen Khachanov, the world number 40 from Russian Federation.
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