Wawrinka edged Tsitsipas 7-6 (6), 5-7, 6-4, 3-6, 8-6 after 5 hours and 9 minutes of breathtaking tennis in sweltering heat to reach the quarter-finals at a Grand Slam tournament for the first time in two years.
Federer, a 20-time major victor, is the oldest man to make the quarter-finals of a Slam since Jimmy Connors at the 1991 US Open.
Exhausted as he was by a match finally decided by a backhand that floated past Tsitsipas and landed on the outside edge of a line, Wawrinka still possessed the energy to joke about facing Federer, who has won 22 of their previous 25 meetings.
Federer is chasing a record-extending 21st Grand Slam title.
"I was prepared for the worst scenario, losing in the first round in three sets". "He beat me in three sets with his awful shorts".
Panic as Apple shuts down iTunes
There is a chance that Apple will not be able to deliver all of these updates in time for the release date. The new operating system will include separate apps divided into Music, Podcasts, TV and Books.
Last year, the three-time Grand Slam champion, following injury struggles, lost in the first round to Guillermo Garcia-Lopez and dropped out of the world's top 250.
Federer, the 2009 champion in Paris, is playing at Roland Garros for the first time since 2015. "I feel very disappointed", said Tsitsipas, who upset Federer at the Australian Open in January en route to his first Grand Slam semifinal.
"I hope he's not at the level of '15, but we'll find out, because there he was crushing the ball".
The 37-year-old Swiss duly dispatched the youngster although he was pushed to a tiebreak in the third set on his way to becoming the oldest player to reach the fourth round since Nicola Pietrangeli in 1972 with a 6-3 6-1 7-6 (8) victory. "So close. I gave him room to do whatever he likes, all those break points", Tsitsipas said, pausing frequently between words.
Nadal won by the same score as Federer, but he was at least given a little bit more of a test by another unseeded Argentine, Juan Ignacio Londero. In his second loose service game since the start of the match, Nadal suffered a break in the next game when his forehand landed long but that could not have stopped him, firing a forehand victor for a break in game nine and the place in the quarter-final.
Elsewhere on Sunday, Nadal is taking on Argentina's Juan Ignacio Londero while seventh seed Kei Nishikori is pitted against French number four Beniot Paire. The 19-year-old Vondrousova beat 12th-seeded Anastasija Sevastova of Latvia 6-2, 6-0 in just 59 minutes.
The clay courts of Roland Garros host the second Grand Slam of the season.