Zverev, a Roland-Garros quarter-finalist in 2018 and 2019, has now made the second week in Paris for a fourth year in a row.
He will next square off against Japan's Kei Nishikori, who finally got through a match in less than five sets when his opponent Henri Laaksonen retired with a surprise injury while down 5-7.
"We could do this four more times next week and then it's perfect," Zverev jokingly told Marion Bartoli when she pointed out that she was conducting his on-court interview for a third consecutive match this week in Paris.
"I was down 5-3, 40-0 on his serve, so you don't always come back from that score. He played a fantastic match, he's playing great on this surface anyway, so I knew I had to play much, much better than the first two rounds and I did that today.
"I'm happy that the further we go in the tournament, the better I'll start hopefully playing."