The Serbian saw off unseeded Italian Salvatore Caruso 6-3, 6-3, 6-2, AFP reported.
"Finally, I think I found my best form in the second set," said Djokovic, who is yet to drop a set in the tournament after straightforward wins over Hubert Hurkacz and Swiss lucky loser Henri Laaksonen.
"It's good, I'm very motivated here at Roland Garros, the most beautiful tournament in the world."
It is the 10th successive year the top seed has reached the second week – and 13th in total – as he looks for a second French Open title after sealing his first 'Djoko' Slam in Paris in 2016.
Djokovic was never in any real trouble against world number 147 Caruso on Court Philippe Chatrier, breaking serve five times in the match and saving all of the five break points he faced.
The 32-year-old finished with eight aces and 25 winners against an outclassed opponent.
World number one Naomi Osaka's hopes of winning a third successive Grand Slam ended Saturday when she was knocked out of the French Open in the third round by unheralded Katerina Siniakova of the Czech Republic.
Japanese top seed Osaka, the reigning US and Australian Open champion, crashed to a 6-4, 6-2 defeat to the 42nd-ranked Czech.
Osaka was undone by a shocking 38 unforced errors as she finally ran out of luck in Paris having had to come back from a set down in her first two matches.
"It's amazing, I can't believe it, I am so happy now," said Siniakova, who was the women's doubles champion in Paris in 2018 alongside Barbora Krejcikova.
"I played my best tennis and I hope it continues."
Osaka dropped the first set for the third successive match at the tournament, squandering seven break points in all.
Despite being seeded top for the first time at a Slam, the 21-year-old Osaka had never looked convincing in Paris.
She was two points away from defeat in the first round against Anna Karolina Schmiedlova and came back from a set and break down to see off Victoria Azarenka in round two.
Her defeat also means that only four of the top 10 seeds in the women's singles are left in the tournament.