Djokovic appeared to be troubled by the searing heat and needed four sets to reach the second round – 6-3, 3-6, 6-4, 6-0.
The Serbian moved seamlessly through the gears in the final set and will now play Tennys Sandgren next on Thursday.
Djokovic is widely considered one of the favourites to prevail at Flushing Meadows after his recent resurgence which has included beating Roger Federer in the Cincinnati Open final earlier this month.
And Djokovic has explained how deep he had to dig in order to overcome Fusovics.
“It was hard for the first two-and-a-half to three sets,” Djokovic said.
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“I think after the third set we started to play a little bit better, at least from my side I started hitting the ball a bit better.
“It was survival mode really. Credit to Marton for fighting well.
“He is great fighter and he deserves round of applause for his performance today.
“I was actually praying that the next moment I got to feel better.
“I wasn’t feeling great for most of the three sets.
“But you have these kind of days and these kind of matches.
“A lot of players struggled today and you just have to deal with it.
“It is not easy but it is what it is and I’ll take this win and I want to thank everyone for their support and patience to stay and watch the match until the end.”