But he hadn't been past the fourth round at a Slam since, in part because he missed time after knee surgery. "You don't want to be in my place", Tsitsipas said.
Federer, the 2009 champion in Paris, is the oldest man to make the quarter-finals of a Grand Slam tournament since Jimmy Connors at the 1991 US Open.
Four years ago, Federer lost in the quarterfinals to Swiss countryman Stan Wawrinka in straight sets.
Wawrinka's run to the quarter-finals would have looked unlikely this time past year when the legacy of two knee surgeries in 2017 saw him lose in the first round in Paris.
"I have some bad memories against Stan in 2015", said Federer.
"I was prepared for the worst scenario, losing in the first round in three sets".
Rafael Nadal ended the dream run of French Open debutant Juan Ignacio Londero with a typically dominant 6-2 6-3 6-3 victory on Sunday to power into the quarter-finals. Serving at 75%, Nadal lost only six points on serve in the opening set, defending three break points in game five when he was already in front and mounting the pressure on Londero after taking nearly half of the return points.
They had shared that record with Budge Patty but moved above the American with two more dominant displays, although 11-times champion Nadal did drop his first set of the tournament. Nadal has only been defeated twice in his French Open career and the 78th-ranked Londero never looked like becoming the third man to achieve the feat.
Romanian third-seed and reigning champion in Paris Simona Halep leads the charge in the other side of the draw, along with Australian Ash Barty - both of whom play their fourth-round ties on Monday.
The 2017 US Open victor is now the clear favourite in her half of the draw after the exits of world number two Karolina Pliskova and one of the pre-tournament favourites Kiki Bertens of the Netherlands.
She will face 31st seed Petra Martic for a semi-final spot, after the Croatian followed up her third-round upset of second seed Karolina Pliskova by coming from a set down to beat Estonia's Kaia Kanepi.
Czech teenager Marketa Vondrousova reached her maiden major quarter-final by thrashing Anastasija Sevastova 6-2, 6-0.
At least five women will reach their first Roland Garros quarter-final this year, the first time that has happened since 2001.