The two-time champion missed last year's tournament with an elbow injury but beat Marton Ducsovics in straight sets on Arthur Ashe Stadium.
Djokovic won through 6-3, 3-6, 6-4, 6-0 in a match that lasted three hours played in temperatures reaching 40 Celsius.
The Serb was delighted to take a break towards the end of the match and said: “I want to thank the US Open for allowing us to have a 10 minute break at the third set.
"We both needed it but the rule is we can’t speak to our team members in the locker room.
“My physio was a couple of feet away and we were winking at each other and giving each other signs! It’s funny but Marton and I were in ice baths next to each other.
“It was a wonderful feeling to battle with a guy for two-and-a-half hours and the match isn’t over and you’re sitting naked.
“We obviously both struggled for two-and-a-half to three sets. Towards the end of the third we started playing better, at least from my side.
“A lot of players struggled and you have to deal with it. I’ll take the win and I want to thank everyone for their support and patience."
Players scrambled for relief from the heat and some retired from their matches when they couldn't find any in red-hot New York.
The No 6 seed Djokovic headed to a fourth set with Ducsovics after the players took a break following the third.
Djokovic, who lost the 2016 final to Stan Wawrinka, could face a quarter-final against No 2 seed Roger Federer.
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