Djokovic wants to win the Roland Garros title more than any other, and few would bet against him if he can maintain the form he showed in a 6-1 6-4 6-1 victory.
The second seed had dropped a set against Marin Cilic in a long match in the previous round while Tsonga had seen off Jerzy Janowicz in straight sets.
Djokovic raced into a 5-0 lead and took the set 6-1. Tsonga’s only moment of hope came when he pulled back from 2-5 to 4-5 in the second set. Djokovic snuffed out the comeback, though, and then raced through the third set to clinch victory after only an hour and 29 minutes.
Next he will play eighth seed Milos Raonic, who reached his first grand slam quarter-final with a 6-3 6-3 6-3 win over Marcel Granollers.
Roger Federer was dumped out by Ernests Gulbis, who fought from a set down to claim a 6-7 (5/7) 7-6 (7/3) 6-2 4-6 6-3 victory.
Andy Murray battled past Germany’s Philipp Kohlschreiber and into the fourth round. The pair were locked at 7-7 in the deciding set as darkness halted the match on Saturday, resuming on Sunday morning. After 40 minutes of tense, competitive tennis the Scotsman emerged a 3-6 6-3 6-3 4-6 12-10 winner.
In the women’s, favourite Maria Sharapova came from a set down to beat Sam Stosur 3-6 6-4 6-0 and reach the quarter-finals.