Zverev who is seeded second for the French Open was given a big scare in the second round on Wednesday.
However, the German prevailed in five sets against world No 60 Dusan Lajovic - 2-6, 7-5, 4-6, 6-1, 6-2 in Paris.
Zverev, who picked up his third Masters title in Madrid last month, has struggled in the Grand Slams to his date, with his best showing coming at Wimbledon last year where he reached the fourth round.
He is widely seen as a natural threat to Rafael Nadal - who is gunning for his 11th French Open crown - on clay.