World number one and top seed Djokovic defeated 79th-ranked Schwartzman 6-1, 6-2, 6-4, wrapping up the marquee match on Arthur Ashe Stadium court minutes before midnight.
"I hope it was a midnight delight," the reigning Wimbledon champion told fans, although in truth the contest offered little drama.
Schwartzman, playing just his second Grand Slam tournament and his first tour-level hardcourt event, pulled the Serbian star into rallies from the baseline, even breaking him for his only game of the opening set.
"I thought I hit the ball very well throughout the whole match," Djokovic said. "I'm very pleased. It's never easy to start a US Open smoothly."
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That was the common refrain on the opening day, as former champions Andy Murray, Maria Sharapova and Venus Williams also advanced, taking center stage with two-time defending champion Serena Williams and five-time champion Roger Federer due to launch their campaigns on Tuesday.
"I could have easily lost that match," said Murray, who thought he'd have been in real trouble in a fifth set. "I was very close to losing the match."
Murray twice fought back from a break down in the fourth -- Haase unable to press his advantage at 4-1 and again at 5-3 even as Murray could be seen clutching various areas of his body on shot after shot.
"I don't know exactly why it happened today," said Murray, who trains in the steamy heat of Miami and didn't think the 30 C temperatures on Louis Armstrong Stadium were excessive. "At the time it happened I wasn't exhausted.