The German was too good for French world No.103 Lucas Pouille in one of the headline acts on Rod Laver Arena on day one of the Open, winning 6-4 6-4 6-4.
Zverev has twice reached the final of a grand slam - at last year's French Open and at the 2020 US Open - while he's also reached the semi-finals eight times, including his second Melbourne last-four appearance last year.
But the 27-year-old has so far been unable to lift the trophy.
Zverev, who warmed up for the Open in the German line-up at the United Cup, wasn't at his best against Pouille -- but he didn't need to be.
While the Frenchman, who has been ranked as high as No.10 in an injury-ravaged career, pulled off some spectacular shots, Zverev mostly had all of the answers and his serve was firing, with 18 aces
His rival only had two break point opportunities through the match, both in the third set, which Zverev handled with aplomb.
The German said that Pouille, who has battled back problems among his injuries was always a tough opponent, particularly when fit.
Pouille was a semi-finalist at Melbourne Park in 2019 and has reached the quarter-finals at both Wimbledon and the US Open.
"Playing Lucas, he's somebody when healthy who is not the ranking that he is," Zverev said.
"He's a great player so I wish him all the best."
Zverev will play world No. 43 Pedro Martinez in the second round, with the Spaniard's opponent Luciano Darderi withdrawing for medical reasons while trailing 6-3 4-1.
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