"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", said Zverev, who will face in-form Russian Daniil Medvedev for the title.
The 23-year-old Russian, runner-up at this year's US Open, ousted Tsitsipas 7-6, 7-5.
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"I did say before this year and during this year in the beginning that Sascha (Zverev) was the best in our "Next Gen" group", the world number four said.
"I didn't make him defend enough".
The history was with Medvedev but there was nothing in it as he and Tsitsipas entered the first-set tie break after 43 minutes of high-quality tennis. Federer, who was given a warning for "unsportsmanlike conduct" at the end of the second set, vented at the umpire after not being told new balls were in play.
The young Greek proved to be too strong for Djokovic, overcoming a slow start and playing against only one break point in the entire encounter to mount the pressure on the Serb who couldn't endure it, losing 3-6, 7-5, 6-3 in just over two hours to end his run in the quarters and get some well-deserved rest.
Victory confirms Tsitsipas' debut at next month's ATP Finals in London.
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"It's a great achievement, I'm proud of myself and, hopefully, I get the win tomorrow", said Medvedev.
Medvedev said of Fognini's remark: "If some top players like Fabio can say this about me, it shows that I'm on the (right track), I'm playing (well) and it's not easy to play against me". "He was the better player in the second and third sets".
"When I was serving for the match, he changed it again, surprised me again, which I made some mistakes that I shouldn't do but I'm really glad to be in the final after a tough match".
Zverev, meanwhile, followed up his quarter-final win over Roger Federer with a more straightforward last-four triumph over Matteo Berrettini.
"He's different this year than previous years", said a wary Zverev.
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