Giving away 14 years to the swashbuckling young Greek on a baking afternoon, 2015 champion Wawrinka prevailed in a riveting five-hour battle of the backhands in front of an enthralled Court Suzanne Lenglen crowd.
Tsitsipas, 20, looked on the brink of victory at 5-5 in the fifth set but could not convert any of the three break points that came his way and 28th seed Wawrinka went on to claim a 7-6(6) 5-7 6-4 3-6 8-6 victory.
Tsitsipas ended up coated in claydust after several diving volleys and the drama went right down to the last point when Wawrinka's sliced backhand pass just touched the sideline -- leaving Tsitsipas crestfallen.
"That's the reason I came back from (knee) surgery," three-time Grand Slam champion Wawrinka said after the classic. Today was something really special."
Sixth seed Tsitsipas admitted defeat, when he was playing such scintillating tennis, had left him in tears.
"It's the worst feeling ever," he said.
Third seed Federer, bidding to emulate his 2009 French Open title, was sublime in the dazzling sunshine, waltzing past Argentine Leonardo Mayer 6-2 6-3 6-3.
The 37-year-old is still to drop a set but Wawrinka is the last player to beat him at the French Open -- four years ago --since when Federer has skipped the tournament.
"I hope he's not at the level of '15, but we'll find out,
because there he was crushing the ball. It was unbelievable," Federer told reporters.
Defending champion Rafael Nadal was equally impressive during a 6-2 6-3 6-3 win over Argentine debutant Juan Ignacio Londero, reaching his 38th Grand Slam quarter-final.
He will face the winner of the match between Kei Nishikori and Benoit Paire which was stopped for bad light.
Former women's champion Garbine Muguruza had been looking ominously good thanks to a return top form but her hopes were dashed by 2018 runner-up Sloane Stephens on Sunday.
American Stephens won 6-4 6-3 to line up a clash with Johanna Konta who became the first British woman to reach the last eight at Roland Garros since 1983 by beating Donna Vekic.
Left-handed Czech teenager Market Vondrousova reached her first Grand Slam quarter-final in stunning fashion -- thrashing Anastasija Sevastova 6-2 6-0.
She will play Croatia's Petra Martic who rallied from a set down to beat Estonian Kaia Kanepi 5-7 6-2 6-4.
The heat of the weekend is forecast to disappear on Monday when the rest of the fourth-round is completed.
Men's top seed Novak Djokovic faces Jan-Lennard Struff while women's defending champion Simon Halep, the clear favourite for the title after an exodus of big seeds, takes on unseeded Pole Iga Swiatek.
(Reporting by Martyn Herman, editing by Ed Osmond)
