Rublev served for the first set at 5-3 up but the 13th seed fluffed his lines. But he still led 5-4.
Handed the reprieve, Tsitsipas held his own serve to draw level and then claimed Rublev’s serve to take a 6-5 lead.
The Greek notched up his fourth consecutive game to claim the opener 7-5 after 50 minutes on Court Philippe Chatrier.
From 2-2 in the second, Tsitsipas rolled another four consecutive games to take it 6-2.
Advantage
After 82 minutes he was in the driving seat against the 22-year-old Russian.
An early break of serve gave him the advantage in the third and he did not relinquish his grip.
He wrapped up the encounter in one hour and 52 minutes.
“I remembered what fighter I am,” Tsitsipas recalled of his first set relaunch. “I put my brain to work to try and find the solutions.”
Tsitsipas will play the winner of the second quarter-final in the top half of the draw between the top seed Novak Djokovic and the 17th seed Pablo Carreno Busta.
The pair met at the US Open in September and Carreno Busta registered his only win over the Serb in four meetings when Djokovic was disqualified for hitting a ball at a line judge.
