The Wimbledon champion, who won only two matches on the North American hard courts after getting married days after his All England Club triumph last month, sprinted to victory in 97 minutes.
"I'm very pleased," Djokovic told the Arthur Ashe Stadium crowd after the one-sided win. "It's never easy to start a U.S. Open smoothly."
Seven-times grand slam winner Djokovic, who won at Flushing Meadows in 2011, made it look easy in a masterful display with 24 winners including seven aces against Schwartzman, who was playing his first tour-level match on the surface.
Djokovic admitted that he had struggled to get his mind on the game with all the changes in his life, including the expected arrival of their first child in a couple of months.
"I didn't have much time to think about tennis with all this happening," the 27-year-old Serb said. "It is a new chapter for my wife and I, and we are very excited."
Djokovic, who has thrived on hard courts, with four Australian Open crowns on his resume, fell in the round of 16 in his two warm-up tournaments after receiving first-round byes.
"The last three weeks actually, Toronto and Cincinnati, were a bit tough emotionally for me," he said. "I wasn't finding my game. I wasn't able to feel comfortable on the court.
"I probably was not mentally ready to still compete at a high level. But now it's different. I feel emotionally recharged and ready to go."
The Serbian world number one will next play Paul-Henri Mathieu of France, who was extended to five sets by Gilles Muller of Luxembourg in a match that included three tie-breaks.
(Reporting by Larry Fine; Editing by Greg Stutchbury)
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