The German fourth seed fought back to win 4-6, 6-1, 5-7, 7-6, 6-2 after four hours and 11 minutes and set up a quarter-final against Alex de Minaur.
It was the second-latest finish in the tournament's history - after Novak Djokovic's win over Lorenzo Musetti which finished at 03:07 local time on Sunday morning - ending at 01:40.
"What a match," said Zverev. "I'm lucky to be through."
He will be targeting a fourth straight Roland Garros semi-final after making the last eight for the sixth time in seven years.
He also beat Tallon Griekspoor in a deciding set, in which he trailed by a double-break at 4-1, in the third round.
"I've played a total of eight-and-a-half hours over the last three days so I need to recover," said Zverev.
"I need to do everything possible to be ready for the quarter-final match."
Zverev is playing under the shadow of an ongoing trial in Berlin over allegations of assaulting an ex-girlfriend, who is the second woman to accuse him of abuse.