Dimitrov, the world No. 4 who is celebrating his 27th birthday on Wednesday, also lost his first-round match at last week's Madrid Open.
Rafael Nadal powered his way into the third round of the ATP Italian Open on Wednesday with a 6-1, 6-0 win over Bosnian Damir Dzumhur.
"It's not easy to come from Madrid where there's a lot of altitude and it's very fast", said Zverev. Top seed Nadal recorded his 20th clay-court win of the year while Shapovalov will at least have the consolation of becoming the Canadian number one on Monday.
It was not even as close as the five games Nadal lost suggested. He saved the first break point and delivered an ace serve to deuce.
Berrettini turned on his right ankle at 1-2 in the second set and looked in difficulty, allowing Zverev to push through.
Svitolina also reached the quarterfinals, overcoming a poor start to beat 14th-seeded Daria Kasatkina 0-6, 6-3, 6-2. The Madrid loss was clearly an aberration and Rafa is definitely looking determined to head to Paris with an eighth title on claycourts of Rome. "And that's what I did today", said Nadal, who is targeting an eighth Rome title and first since 2013.
After a surprise summer loss a year ago to Denis Shapovalov, Rafael Nadal gained revenge on his surface, slamming the Canadian 6-4, 6-1 to reach the Rome Masters quarterfinals.
Djokovic, a four-time champion on the comeback trail three months after elbow surgery, eased past Georgia's Nikoloz Basilashvili 6-4, 6-2.
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The 22-year-old Kontaveit won through 6-2, 7-6 (7/3) against the 37-year-old American who was seeded eighth in a tournament she won almost two decades ago to 1999.
The 21-year-old managed to beat Kyle Edmund of Great Britain, who knocked out 12-time Grand Slam champion Novak Djokovic of Serbia at the recent Madrid Open, by a 7-5, 7-6 scoreline.
In women's action, Simona Halep routed Naomi Osaka 6-1, 6-0 for the first of two wins she needs this week to keep Caroline Wozniacki from taking her No. 1 ranking.
Halep next plays 13th-seeded American Madison Keys, who battled past Croatian Donna Vekic 7-6 (7/2), 7-6 (7/0), for a place in the last eight.
"It was a positive match, of course", said Nadal, as quoted by the Express.
By contrast, Sharapova needed two and a half hours to master 18th-ranked Barty 7-5, 3-6, 6-2 in their first round match.
Elsewhere in the men's event, number five seed Juan Martin del Potro of Argentina exited the tournament as he had to retire hurt from his match against ninth seeded Belgian David Goffin.More news: Red alert raised after ash bursts from Hawaii volcano
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