The 33-year-old Serb won 6-4, 6-3, 6-3 in two hours and 23 minutes under the roof on Court Philippe Chatrier.
“It was a very even match despite what the scoreline suggests,” said Djokovic. “I was just a little bit better with my service games when it mattered.”
The Serb opted to break up the rhythm of the hard-hitting Russian with drop shots and slices. It paid dividends.
“Obviously I had to do something like that because he has a lot of power,” Djokovic added. “I am happy with my tournament so far but I have to prepare well for the next match.”
Djokovic, who has yet to drop a st in the 2020 competition, has been in the last eight at the French Open a total of 14 times. And he will play either the 17th seed Pablo Carreno Busta or Daniel Altmaier, who emerged from the qualifying competition.
Their last 16 match on Court Suzanne Lenglen was delayed due to persistent rain.
Fifth seed Stefanos Tsitsipas and 13th seed Andrey Rublev advanced to the last eight in Paris for the first time on Monday after victories over Grigor Dimitrov and Marton Fucsovics respectively.
