In the second round, Novak took down Denis Shapovalov 6-3, 6-3 in 70 minutes, dropping eight points on serve and taking nearly half of the return points to dominate all the time, breaking Denis three times and moving over the top to set the third-round clash with John Isner.
The latest win means Medvedev enters a sixth-straight, where he will aim to win his second Masters title after claiming August's Cincinnati trophy.
Djokovic sits at the top of the rankings at the moment but trails Rafa Nadal in the yearly standings and, with the Spaniard absent from Shanghai, had hoped to make up significant ground in China.
"(All) you can do is hit as hard as you can side to side, be accurate and make him move, otherwise you can just play it back to him.it just keeps coming back".
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.
Zverev leads an imposing 4-0 head-to-head record with Daniil Medvedev, all of which were played on hard courts, but the he has not faced the world number four since the Rogers Cup previous year and Medvedev is a wholly different proposition now.
"I didn't feel bad", said Tsitsipas, who has yet to beat Medvedev after five career meetings. "Positions have changed a little bit so I think I can contest him right now". But the German defeated 20-time Grand Slam champion Federer on Friday and took that momentum into his last-four clash with the 23-year-old Berrettini.
It's been a disappointing week where not much has gone for us, and indeed not much has gone for the big names in the draw, with Novak Djokovic and Roger Federer dumped out on Friday by young players with ambitions to dethrone the elite duo eventually.
"It's so boring that I hate myself for putting myself into that kind of situation where I have to play on his terms and not on my terms". "He's been playing some unbelievable tennis in the last few months".
It's a mark of how their two levels have become considerably closer that in that match in 2018, Zverev was priced around the [1.15] mark pre-match, a rather large difference to the current market pricing.
"He had the high-quality tennis and he played well after his serve".
Nadal, the World No 2 and victor over Medvedev at Flushing Meadows, is not in Shanghai because of a wrist injury. Tsitsipas has beaten the best player in the world to reach the Shanghai Masters semi-finals, as well as qualifying for the ATP Tour finals.