Djokovic, chasing the only grand slam title to elude him, was never troubled by the 13th-seeded Tsonga, who suffered an embarrassing defeat in 89 minutes one year after making it to the last four in Paris.
The Frenchman's ordeal ended on the first match point when he sent a backhand long as Djokovic reached the quarter-finals of a grand slam for the 20th consecutive time.
In 2012, Djokovic needed five sets to see off Tsonga in the quarter-finals and the Serbian had no intention of letting that happen again.
"The performance was great from the start till the end. I came with the exact level of intensity that I was looking for before the start of the match," said Djokovic, who converted seven of nine break points.
"Two years ago was kind of a similar situation where I started very well, won the set 6-1 and I was 4-2 up and then he managed to come back. Then we had the tough match and that ended up in five sets," he told reporters.
"I didn't want the similar scenario."
Tsonga paid the price for poor preparations having lost in the second round at the Madrid Masters and the third round at the Rome Masters last month.
"It does hurt. After the match, I mean, I had lots of thoughts in my mind. But I have to continue. I need to hang on," he said.
Watch all the action from the French Open on up to court seven on the Eursport Player.
Results from the French Open Men's Singles matches on Sunday
2-Novak Djokovic (Serbia) beat 13-Jo-Wilfried Tsonga (France) 6-1 6-4
18-Ernests Gulbis (Latvia) beat 4-Roger Federer (Switzerland) 6-7(5) 7-6(3) 6-2 4-6 6-3
6-Tomas Berdych (Czech Republic) beat 10-John Isner (U.S.) 6-4 6-4 6-4
8-Milos Raonic (Canada) beat Marcel Granollers (Spain) 6-3 6-3 6-3
7-Andy Murray (Britain) beat 28-Philipp Kohlschreiber (Germany) 3-6 6-3 6-3 4-6 12-10
24-Fernando Verdasco (Spain) beat 12-Richard Gasquet (France) 6-3 6-2 6-3
- Sports & Recreation
- Milos Raonic
- Marcel Granollers