Zverev hit 52 unforced errors as the momentum swung throughout, BBC Sport reported.
Second seed Rafael Nadal had a walkover, with Australian Thanasi Kokkinakis withdrawing with a right shoulder injury.
The three-time champion will play South Korea's Chung Hyeon in the next round.
Australian Nick Kyrgios produced a stunning display of serving as he hit 24 aces in his routine 6-4, 6-2, 6-4 win over unseeded Frenchman Antoine Hoang.
Kyrgios, the 28th seed, has now reached the third round four times but has never made it past that phase. He now takes on unseeded Russian Andrey Rublev, who got through as a result of the retirement of Frenchman Gilles Simon after the first set of their match.
Meanwhile, Zverev will play Slovenian Aljaz Bedene, who beat 29th seed Benoit Paire, in the third round.
Elsewhere, in-form Cincinnati Masters champion Daniil Medvedev recorded his 16th win from the past 18 matches with a 6-3, 7-5, 5-7, 6-3 victory over Hugo Dellien of Bolivia. The Russian fifth seed will now play Spain's Feliciano Lopez.
In women’s singles, American teenage sensation Coco Gauff is set for an intriguing third-round match against defending champion Naomi Osaka after beating Timea Babos 6-2, 4-6, 6-4 on Louis Armstrong Stadium.
The 15-year-old, who came to prominence at Wimbledon, and the Hungarian world 112 produced a superb spectacle.
Gauff broke three times in the opening set before Babos fought back to level.
In a third set of lung-bursting rallies, Gauff crucially broke in the 10th game to seal victory.