Roger Federer also went down to a younger player in Shanghai when he suffered an ill-tempered 6-3 6-7 6-3 loss to Alex Zverev.
US Open semi-finalist Berrettini was beaten 6-3 6-4 in 67 minutes.
A handicap line can be considered, but given Tsitsipas' propensity to play tight sets, it would be much more risky than simply the match win position on Medvedev here. "I just gave him enough time to really dictate the play from the back of the court and he deserved to win".
Medvedev has now reached a tour-leading nine finals in 2019.More news: Take Flight in Latest CHARLIE'S ANGELS trailer
"I thought he took really a lot of good decisions, and he was super fast on his feet today, which I think made it really hard for me to get my freebies and winners off the baseline".
Prior to Friday's match, Fognini said Medvedev was one of the most risky players to face.
Opening the schedule is Tsitsipas against Medvedev, with the Russian, Medvedev actually taking a 4-0 head to head lead into the clash, although Tsitsipas has taken a set in every single clash. "I didn't feel bad", Tsitsipas said.
I lacked, you know, that little bit of, I guess, dynamic movement and acceleration in my shots.
Zverev boosted his hopes of reaching the ATP Finals by reaching his first championship match since May and a first Masters final of 2019.More news: El Camino: A Breaking Bad Movie Review - 7 Ups & 2 Downs
"I knew if I'm going to keep playing the way I played the first two sets, I'm going to have a chance in the third as well".
Meanwhile, Roger Federer saved five set points in the first set as he scrambled to a 7-6 (7), 6-4 win over 13th-seeded David Goffin and advanced to the Shanghai Masters quarterfinals.
Zverev dispatched Berrettini - one of his rivals to secure a place in London - reasonably comfortably as his serve proved key, the Italian not even getting a break point in the match.
Pospisil failed to capitalize on five set points in the first set, including two chances in the tiebreaker.
Zverev beat Andrey Rublev of Russian Federation 6-0, 7-6 (4) in the last match of the night. I felt like I've played some decent tennis this week and being in a Masters 1000 final here in Shanghai is also something very special for me. He was the better player.More news: Want to live longer? You should get a dog