The world number one had to battle to get through the first two sets, but cruised the third to win 6-3 7-6 6-1.
It took Djokovic one hour 50 minutes to book his place in the second round, as he was watched on by his new coach Boris Becker.
The Serbian, who is seeking to win his fifth Australian Open, will face Argentine Leonardo Mayer on Wednesday.
"I know that I haven't played my best, especially in the second set," said Djokovic. "But credit to my opponent who was playing really nice tennis from baseline.
"On the other hand I was a little bit too passive in some stages of the match and was trying to find the proper, I would say, setting and proper balance and footing in the court."
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