Fresh off winning his third ATP World Tour Masters 1000 title at last week's Madrid Open, the World No. 3 needed an hour and 31 minutes on Wednesday to defeat the 103rd-ranked Italian, reports Efe.
Berrettini had topped American qualifier Frances Tiafoe 6-3, 7-6 (7-1) in first-round action on Monday.
Zverev, who made history on Sunday by becoming the first player to win a clay-court Masters 1000 event without dropping a single service game, kept that streak going by saving three break points in the first set and one more in the second set on Wednesday.
Four-time champion Novak Djokovic of Serbia reached the third round of the Italian Open tennis tournament after defeating Georgia's Nikoloz Basilashvili 6-4, 6-2.
The former world No.1 needed 76 minutes to beat his Georgian rival, ranked world No.74, reports Efe news agency.
Djokovic, world No.18, is set to play the third round against Spaniard Albert Ramos Vinolas, world No.41.