The Tokyo Olympic gold medallist won 6-2, 6-1, breaking his 43rd-ranked opponent four times on the grass at the traditional Wimbledon warm-up event.
A two-time finalist at the Halle Open, Zverev's march was only halted by an incident in the stands when an advertising board fell onto a spectator.
The German second seed was quick to react, handing an ice pack into the stands to help treat the injured man, who was applauded as he left the stadium.
"It was a great match from me," Zverev said, adding, "I felt like I didn't let him play that well, which was important.
"A good start to the tournament, and I'm looking forward to tomorrow."
Zverev, who was eliminated in four sets in the quarter-finals of the French Open earlier in June, will face Italian Lorenzo Sonego in the next round.
Later on Wednesday, Daniil Medvedev became the first player to reach the Halle Open quarter-finals, when he beat France's Quentin Halys in straight sets.
The 2021 US Open winner, now ranked 11th in the world, won 6-2, 7-5 in an hour and six minutes.
In the last match of the day, Stefanos Tsitsipas was dumped out of the tournament by Alex Michelsen, losing 7-6, 7-5 in a close encounter.
On Tuesday, world number one Jannik Sinner rebounded from his epic French Open final loss to Carlos Alcaraz with a straight-sets win over Yannick Hanfmann.
The Italian will face 2023 Halle champion Alexander Bublik in the last 16 on Thursday.