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.
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.
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.