Zverev, the runner-up at the recent French Open, came through 6-4, 6-4, 7-6 (17/15) -- with the tie-breaker taking more than 20 minutes to complete -- to make the fourth round for the third time.
However, the 27-year-old suffered a worrying moment at 2-2 in the second set when he slipped and fell, appearing to twist his left ankle and jar his knee as he sprinted towards the net on Centre Court.
Zverev was treated by the physio and then took a medical timeout at the end of the second set.
The German star needed six match points to seal the deal while saving five set points in the third set tiebreaker.
In a masterful serving display, Zverev didn't face a single break point and clubbed 15 aces in his 52 winners.
Zverev, who has never made it past the fourth round at Wimbledon, will face either US 13th seed Taylor Fritz or Alejandro Tabilo of Chile for a place in the quarter-finals.
