Alexander Zverev, who has reached at least the quarter-finals in five consecutive French Opens, swatted aside Tomas Machac 6-4, 6-2, 6-2 in the night match.
The German second seed will continue his latest tilt at a maiden Slam title against Frenchman Quentin Halys.
Czech Jakub Mensik, the only player other than Djokovic to beat Sinner this year, needed eight match points before eventually downing Mariano Navone 6-3, 2-6, 6-4, 1-6, 7-6 (13/11) to book a meeting with eighth seed Alex de Minaur.
Mensik collapsed on the court after the match with exhaustion and cramp as the Paris heatwave continued to take its toll.
“It’s insane to play in this weather, especially in front of the sun, to be there for more than four and a half hours, it’s just insane,” Mensik said.
Rising Spanish star Rafael Jodar reached the third round of a Grand Slam for the first time, seeing off James Duckworth 6-1, 6-7 (5/7), 6-4, 7-5.
Two-time losing finalist Casper Ruud was back to full fitness after struggling with the hot weather in the first round, taking just three sets to get past Hamad Medjedovic.
Australian Open champion Rybakina blew a one-set lead to exit in dramatic fashion, slumping to a 3-6, 6-1, 7-6 (10/4) loss to Ukraine’s Yuliia Starodubtseva.