Federer saved three match points in the second with Zverev serving for it at 6-5, 40-0 and two in the breaker, but the Swiss couldn't capitalize int he third.
Federer received a code violation in the loss.
"He has a very different tennis from most of the players that I have been playing against this year", said Tsitsipas.
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.
And at the Shanghai Masters this week, Murray squandered two chances to serve out the match against Fabio Fognini and lost in a controversial second-round clash. Federer had been 5-0. Federer was given a point penalty for twice smacking the ball into the crowd in frustration.
"So you could write on Twitter, you mean?"
"I don't think Roger Federer's game suits anybody to be honest".
"I never really felt like I had the upper hand over David today", Federer said. "It's exciting. They're great".
"I think be more aggressive because once you get aggressive and they see that you're really going for it, I might even say they get scared", he said.
Until Friday's match, Djokovic had won 24 straight sets in Asia, a run that included last year's Shanghai Masters and the title in Tokyo last week.
One of 26 unforced errors from Djokovic gave Tsitsipas, who produced an array of searing backhand and forehand winners, three break points and he grasped the opportunity to take a 3-1 lead in the third before going on to seal his place in the penultimate round. Tsitsipas will be filled with confidence following his win over Djokovic but the Greek superstar must continue playing his best tennis since Medvedev is in outstanding form. It was an outstanding match between two elite players but Tsitsipas showed his quality to cause a major upset.
World No. 7 Tsitsipas, who qualified for his maiden year-end ATP Finals yesterday, is the youngest player to defeat each member of the Big Three.
But in making the last four in Shanghai, Stefanos Tsitsipas, 21, Alexander Zverev, 22, and the 23-year-olds Matteo Berrettini and Daniil Medvedev made a piece of history. He reached his first Grand Slam final at the U.S. Open, and then won titles in Cincinnati and St. Petersburg.
Medvedev is 28-3 in matches played since the summer hard court swing started after Wimbledon.