To do it, he has had to win three straight five-set matches, rallying from two sets to one down in all of them and defeating Karen Khachanov, 4-6, 7-6 (4), 2-6, 6-3, 6-3, on Sunday.
The 12-time Grand Slam victor defeated Fernando Verdasco at Roland Garros. The German, at 21, has managed to capture three Masters Series titles and rise up to number three in the world.
Djokovic, who won his only Roland Garros title in 2016 to complete a career Grand Slam, was not considered among the pre-tournament favourites following an injury-hit year. But I think we deserve to be part of it'. I mean, probably now the third-best after Rafa and Roger (Federer).
"For me is wonderful".
The 20th seed maintained his ascendancy against an increasingly laboured Verdasco to secure a sixth consecutive win against the 34-year-old, who was seeking a first appearance in the quarter-finals in Paris.
Djokovic looked shaky to start off as Verdasco's thunderous groundstrokes were becoming hard to manage, however, Djokovic, in pursuit of his 13th Grand Slam, managed to overcome Verdasco's fire.
The German, who has previously stated his desire to be the best in the men's game before Nadal and Federer - now ranked number one and two in the world respectively - retire, once again stated his intention to do so during the French Open that is underway in Paris.
The 12-time Grand Slam champion will play Marco Cecchinato in the last eight after the Italian upset Belgian eighth seed David Goffin.
US Open champion Sloane Stephens cruised past Estonian Anett Kontaveit 6-0, 6-2 to book a last-eight spot for the first time.
American 13th seed Madison Keys also reached her first Roland Garros quarter-final with a 6-1, 6-4 win over Romania's Mihaela Buzarnescu.
Keys's close friend Sloane Stephens, the US Open champion, takes on Russia's Daria Kasatkina who put out Wozniacki.
"Hopefully it will get even better".
"Then once you get to the second week, every match obviously has more nerves, and there's more on the line".
But all eyes will be on Monday's showdown between Serena Williams and Maria Sharapova, with the latter trying to end an 18-match losing streak to her bitter rival. It is the seventh time the world number 35 has reached the French Open fourth round, but it is the only Grand Slam tournament where he is yet to make the last eight.