Italian Berrettini described the win as the best of his career as he became the first ATP player to win a match without losing a single game against a top 10 player in 10 years, when David Goffin defeated Tomas Berdych at the Rome Masters in 2016.
“I think it was one of the best performances of my life,” Berrettini said.
“I think I missed three shots in the entire match and it is not easy against a tricky player like Daniil. I think the game plan was perfect and my weapons were working.”
The former Wimbledon runner-up will face Joao Fonseca in the last 16.
Medvedev, who received a code violation for unsportsmanlike conduct and will certainly receive a major fine for his actions, has yet to speak publicly about his action.
It was his first match on a clay court this season, a surface he strongly dislikes, saying in the past that it is for “losers” and compared it to “like a dog in the dirt”.
Two-time Grand Slam champion Andy Murray told Sky Sports UK that Medvedev should be “embarrassed” by his actions.
“It is shocking and it shouldn’t happen but it did,” Murray said. “I don’t know how much effect that will have on him going forward.
“I’m sure he will be pretty embarrassed walking back to the locker room and I’d be wanting to get off site pretty quickly, I think, if that was the performance I put in today.”
Medvedev has a long history with taking it out on racquets, having smashed a couple during last year’s Wimbledon and US Open tournaments among numerous other misdemeanours during his career.