Zverev, who won the bett1HULKS Indoors last week, was serving for the match at 5-3 in the second, before the Frenchman broke serve and went on to take a tight tiebreaker.
The German world number seven regained his focus and claimed the only break in the decider at 3-3. He held his nerve to set up a semi-final encounter against Jannik Sinner with a 6-4 6-7 (5) 6-4 victory.
In the last quarter-final, Canadian fifth seed Felix Auger-Aliassime beat Japan’s Yoshihito Nishioka 6-3 6-4 and will next face Diego Schwartzman for a place in the final.