Zverev defeated Millman in the first two sets 7-6, 6-3, but he ran into trouble in the third set, falling to Millman 6-2.
During the fourth set, Zverev became overcome with frustration after he faltered in a tiebreaker to force a deciding set.
Zverev sat down at the changeover between sets and smashed his racket on the clay surface. That earned him a warning from the umpire.
It was not the first time Zverev acted out during the win. Earlier in the match, he threw his racket onto the court. He did not receive a violation because the racket did not break.
Zverev needed just over four hours to defeat Millman, winning the match 7-6(4), 6-3, 2-6, 6-7(5), 6-3 to advance.
Last year, Zverev made it to the quarter-finals in Paris, but has struggled since defeating top-ranked Novak Djokovic to win the ATP Finals in November.
The win over Millman sets up a second-round match for Zverev with Swedish qualifier Mikael Ymer on Thursday.