The Serbian star, who is a font-runner for the title this year, has now won 24 consecutive matches without losing in 2020.
Earlier, fifth seed Alexander Zverev defeated Kevin Anderson 7-6(7/2), 5-7, 6-3, 7-5.
Djokovic gave a run for the money to Bosnia-Herzegovina's Damir Dzumhur throughout the match at the Arthur Ashe Stadium in New York.
Notably, he took mere 23 minutes to win the first set before clinching victory in an hour-long second set.
Prior to US Open, Djokovic secured a record 35th title at a Masters 1000 tournament by winning the Western and Southern Open.
Elsewhere in the draw, Germany's Alexander Zverev labored to a close victory, following a three-hour tussle with the 2017 runner-up Kevin Anderson.
The German bagged the first set on a tie-break 7-6 (7/2), while he lost the second set 5-7.
Eventually, Zverev bounced back in the following two sets, beating the South African veteran 6-3 and 7-5 respectively.
Fourth seed Stefanos Tsitsipas also made it to the second round with a straight-set win (6-2, 6-1, 6-1) over Spain's Albert Ramos-Vinolas.
The fourth-seeded Greek stormed past the latter in a little less than two hours.
Also, Tsitsipas lost just four first-serve points (35/39), breaking the Spaniard seven times.
Notably, he won 53 per cent of return points (43/77).
Teen sensation Coco Gauff lost 3-6, 7-5, 4-6 to Anastasija Sevastova in Round 1.
The 31st-seeded Sevastova sent Gauff to her earliest exit from a Grand Slam tournament in four appearances.
Gauff had never lost in the first two rounds in a Grand Slam event.
Meanwhile, two-time champion Naomi Osaka managed to to pull off a three-set victory (6-2, 5-7, 6-2) over Misaki Doi.
Love Sports news?
Subscribe to stay updated.