Victory over world No. 16 Khachanov — an opponent who beat him in the 2018 Paris Masters final — hands Djokovic a meeting with either Pablo Carreno Busta or Daniel Altmaier in the final eight.
It also means Djokovic will contest his 14th quarterfinal in Paris, a record he shares with Rafael Nadal.
Both players were pre-tournament favorites and appear to be on a collision course to face off in the final after Nadal reached the quarters on Sunday. The Spaniard is also yet to drop a set at this year’s French Open.
On Djokovic’s side of the men’s draw, Stefanos Tsitsipas and Andrey Rublev also booked places in the quarterfinals with respective victories over Grigor Dimitrov and Marton Fucsovics.
In the women’s draw, Petra Kvitova overcame Zhang Shuai 6-2 6-4 to reach her first Roland Garros quarterfinal since 2012 where she will face maiden quarterfinalist Laura Siegemund.