Monfils increased his lead to 4-2, but Anderson responded by winning the next three games in a row, before the Frenchman held his serve to take the score to 5-5.
Should No. 103 Mackenzie McDonald defeat former runner-up Milos Raonic later Monday, it will be the first time since 2000 that two men outside the top 100 have made the Wimbledon quarterfinals. A former world number 15, she talked about retiring a year ago, saying that tennis "just wasn't fun" any more and that her main goal in 2018 was to feel good.
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.
"It was good to have that, you are hearing all these things and thinking, "I could be there one day", Draper said after his own straight-sets win over Henry van der Schulenburg.
Roger Federer, the 36-year-old defending champion, knows it is his Wimbledon to lose. "I guess there are other factors that play in".
"It's obviously not easy. I feel physically, mentally ready, fit, positive". I'm a big player, big serve. "When I am playing better, the opponents normally play worse", was his succinct take on matters. "Also at the same time try to treat it like another tennis match".
On the women's side of the draw, Serena Williams is back in the Wimbledon quarterfinals for the 13th time after beating Russian qualifier Evgeniya Rodina 6-4, 6-2.
"I was listening to Roger earlier in the week".
Anderson also said he felt nervous as he faced the big moments against Monfils, but would be anxious if that had not been the case. ICC shared a screenshot of the Test batting rankings which showed the 20-time Grand Slam victor Federer as the No. 1 batsmen in the world.
"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.
The All England Club has come under increasing pressure to rethink its 2pm (1300GMT) start time for Sunday's men's singles final with the football showpiece in Moscow kicking off at 4pm in the United Kingdom (1500GMT).
"You always tend to play better against better players and I am happy to be back in the second week of Wimbledon".
Keen musician Anderson has travelled with his guitar to London and treated himself to a night at a Jack Johnson concert after reaching the last 16.
The top-ranked player in Greece (a career high No. 35), Tsitsipas is hardly alone in studying Federer for tips.
He added: "I played very well in Queen's (where he finished runner-up) coming into Wimbledon".
"I'm more concerned the World Cup final will have issues because the Wimbledon final is going on", Federer joked.
"It will also be nice to spend a little bit time at home just with my family".