
Zverev, semifinalist for the last three years, had not dropped a set in his opening two matches, including a first-round win over Rafa Nadal, but he was on the back foot when the Dutch 26th seed won the opening set.
The German finally broke serve when leading 5-4 in the second set to level the match and made lighter work of the third set and when Griekspoor took a medical timeout it appeared that Zverev would have little trouble closing out victory.
The Dutch 27-year-old forced a deciding set, however, and held a 4-1 advantage after two breaks of serve before Zverev roared back to win four consecutive games.
Griekspoor kept his nerve to force a tiebreak, but after an enthralling match lasting over four hours on Court Philippe Chatrier, it was Zverev who fired down an ace to clinch the tiebreak.