The second-seeded Serbian superstar, eyeing a record-extending 24th Grand Slam singles title at these championships, booked his place in the last 32 with a 6-4, 6-1, 6-1 victory.
Djokovic needed just 1hr 59 minutes to dispose of Zapata Miralles and will now face fellow Serb Laslo Djere on Friday for a place in the last 16.
In hot and humid conditions on the Arthur Ashe Stadium, Djokovic took his time to wear down Zapata Miralles in a physical first set.
But once into his groove in the second set there was no stopping the three-time US Open champion, with Djokovic polishing off his Spanish opponent briskly.
"I'm still moving pretty well for an old fella," the 36-year-old joked in an on-court interview after his win.
"It was a tough match, especially in the first set. When we had the entire court in shadow, there was a lot of humidity.
"But it's same for both players. I didn't start off the match very well but the second and third sets were a couple of levels higher so I'm very pleased with the way I finished off the match.
"That's why we train several hours a day in humid and hot conditions - trying to get ready for anything that can potentially await you on court. Once you're in the tournament you need to be ready. Even if you think you're not you have to keep telling yourself you are."
Although Djokovic has dropped just 11 games in his two opening matches, the Serbian believes there is plenty of room for improvement as the tournament progresses.
"I still feel I can play better," said Djokovic, who guaranteed he will return to the top of the world rankings with his first round win on Monday.
"But first couple of matches back, straight sets wins - I'm happy to be back.
"At 36 years of age, after 20 years of coming to New York, I still have the hunger to play my best tennis on this court."
