The Serbian superstar struggled to impose himself against the confident Croat on Rod Laver Arena before finally taming the 18-year-old 6-2, 6-7 (5/7), 6-3, 6-4 after a four-hour marathon.
While far from his best, the world number one showed no sign of the right wrist problem that hampered his build-up.
"Well, I started off very well for a 36-year-old guy. But, geez, when you think about it, I'm double his age," Djokovic said.
"Reality hit hard tonight," he added, smiling.
"But credit to him, he had an incredible game plan, he had an answer to everything.
"I had some good moments and other moments I wish I could have played better. Physically, I'm still finding myself on court."
Djokovic surged to the title last year with a three-set victory over this year's seventh seed, Stefanos Tsitsipas.
If he does the same again, he will pass Australian Margaret Court's all-time Slam record and join only Court (Australian Open) and Rafael Nadal (French Open) in winning 11 times at a single major.
Victory stretched his record at Melbourne Park to 90-8 as he reached the second round for a 17th consecutive year.
But he was troubled by Prizmic's speed and booming baseline play, which forced many uncharacteristic errors in a match many thought would be a cruise.
"He deserves every applause, every credit he gets," Djokovic said. "It's amazing to see someone so mature for his age -- he handled himself on the court incredibly well.
'His moment'
"This is his moment, honestly. It could have easily been his match as well. We are going to see a lot of him in the future."
The Croat is the current French Open boys' champion and he used the occasion to showcase his talent, undaunted by a Grand Slam main draw debut on Djokovic's most successful court.
He lost his opening service game, but held his next two before needing a medical timeout for a left thigh problem.
When he returned, Djokovic mercilessly moved him around the court to take the first set in 42 minutes.
Undeterred, the Croat, with his leg strapped, raced to a 3-1 lead in the second set, breaking Djokovic after he was given a time violation, then belting a glorious cross-court winner.
The Serb got back on level terms but it went to a tie-break, where Prizmic took charge, racing 6-2 clear. Djokovic saved three set points but not a fourth.
Djokovic pulled 2-0 clear in the third set, only for Prizmic to keep punching above his weight, winning the next three games.
But the defending champion found a new wind, saving two break points to hold for 4-3 before closing out the set, roaring in delight as he did so.
He broke the tiring teenager immediately in the fourth set before again needing to repel a fightback.
Battling to the end, Prizmic saved six match points before finally succumbing, with Djokovic next playing the winner of an all-Australian showdown between Marc Polmans and Alexei Popyrin.
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