Zverev broke veteran Halys in the Frenchman's first service game in all four sets. The German collected a second break to seal the first two.
But, with a wide-open draw beckoning, Zverev wobbled in the third.
Roared on by the late-night crowd, 90th-ranked Halys, who is from the Roland Garros neighbourhood, fought back and, as the clock passed midnight, forced a fourth set.
Zverev jumped to a 3-0 lead in the fourth set and then broke Halys in a marathon eighth game to win in three hours and 10 minutes.
"I knew I just had to stay with my game and I'm going to get my chances and in the fourth set I did," said Zverev. "I'm very happy I could finish it at 1 am, not 3 am."
The 29-year-old German, ranked third in the world but seeded second at Roland Garros after reigning champion Carlos Alcatraz withdrew, became the top seed still standing when Jannik Sinner lost the night before.
On Friday, the German's match on Court Philippe Chatrier followed the dramatic five-set come-from-behind victory by 19-year-old Brazilian Joao Fonseca over Novak Djokovic.
At the start of the evening, the remaining men had 24 Grand Slam singles titles between them - all of them owned by the 39-year-old Serbian.
Of the last 16, only Zverev and Norwegian Casper Ruud have even appeared in a Grand Slam final, losing three each.
In the next round, when the heatwave that has played such a role in roiling the draw is expected to have passed, Zverev will play 106th-ranked Dutchman Jesper de Jong, who upset 13th seed Karen Khachanov in five sets.
"I hope to give myself the chance to win all the matches I play," said Zverev