The meeting lasted 1 hour 58 minutes and ended with a score of 6: 1, 6: 4, 6: 1 in favor of the first racket of the world.
The next Serbian rival in the tournament will be Briton Kyle Edmund, who defeated the representative of Kazakhstan Alexander Bublik.
Djokovic is a three-time US Open winner.
Earlier it was reported that Daria Kasatkina lost to Ukrainian Marta Kostyuk in the first round of the US Open.