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.
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.
Berrettini, for his part, was competitive with Zverev in the opening set but was unable to keep pace in the second due largely to a low 47 percent winning percentage of first serves.
The 21-year-old Zverev, who has now won 10 straight matches and 20 consecutive sets on clay, on Thursday will take on Briton Kyle Edmund - a 6-2, 7-6 (7-3) winner over Frenchman Lucas Pouille - for a berth in the quarter-finals.
The German has a 2-0 career record against Edmund, having won on clay in Nice in 2016 and on hard courts last year in Beijing.
Zverev captured his first Masters 1000 title at last year's Italian Open, defeating Serbian great Novak Djokovic in the final.
The Italian Open is one of the biggest clay-court tournaments on the ATP World Tour calendar and a key tune-up for the French Open, which gets under way on May 27.
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