Djokovic, the 2016 champion, needed just 83 minutes to complete a 6-1, 6-2, 6-2 demolition of Lithuania’s Ricardas Berankis.
The top seed went level with Roger Federer for victories at the tournament, although still 25 behind Rafael Nadal’s all-time best.
He will now face Colombian lucky loser Daniel Elahi Galan, ranked 153, for a place in the last 16.
“It was difficult for Ricardas in the third set as he had an injury and couldn’t move very well,” said Djokovic whose afternoon stroll was eased by his opponent needing treatment on a back problem after the second set.
“But I felt good just as I did in the first round and I want to continue like that.”
Djokovic, bidding to become the first man in half a century to win all four majors twice, also dropped only five games in his first round match against Mikael Ymer who likened facing the Serb to a “snake killing its prey”.
Victory stretched his 2020 record to 33-1, his only defeat coming via disqualification from the US Open.
Former champion Jelena Ostapenko swept second seed Karolina Pliskova out of the tournament, triumphing 6-4, 6-2 on the back of 27 winners.
Shapovalov loses in five hours
Garbine Muguruza, the 2016 champion from Spain, knocked out Pliskova’s twin sister Kristyna, 6-3, 6-2.
Ninth seed Denis Shapovalov committed 106 unforced errors as he crashed out following a 7-5, 6-7 (5), 6-3, 3-6, 8-6 loss to Roberto Carballes Baena.
Spanish world number 101 Carballes Baena prevailed after a five-hour battle on Court Suzanne Lenglen to set up a clash with 18th seed Grigor Dimitrov.
Shapovalov, who reached the quarter-finals of the US Open, twice served for the match in the final set at 5-4 and 6-5 but was broken three times in succession.
“Scheduling is absolutely awful. It’s just complete trash,” raged the Canadian on having to return to the court later to play doubles.
Dimitrov downed Slovakia’s Andrej Martin 6-4, 7-6 (5), 6-1 to reach the third round for a fourth successive year.
Greek fifth seed Stefanos Tsitsipas, who made the fourth round last year, downed claycourt specialist Pablo Cuevas 6-1, 6-4, 6-2 having needed to come back from two sets down against Jaume Munar in his opener.
Next up for Tsitsipas is Slovenia’s Aljaz Bedene, the world number 56.
Also moving on was two-time Wimbledon winner Petra Kvitova, whose best Roland Garros run was to the semi-finals in 2012.
The seventh seed defeated Italy’s 94th-ranked Jasmine Paolini 6-3, 6-3 to register her 25th French Open win.
Kvitova next faces 18-year-old Leylah Fernandez of Canada, last year’s junior champion, who reached the last 32 of a Slam for the first time by seeing off Polona Hercog 6-4, 3-6, 6-1.
Australian Open champion and fourth seed Sofia Kenin needed three sets to see off Ana Bogdan of Romania, winning 3-6, 6-3, 6-2 while eighth-seeded Aryna Sabalenka of Belarus took down Russia’s Daria Kasatkina 7-6 (6), 6-0.
Kasatkina has now gone two years without beating a top 10 player.
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