Four-time champion Djokovic was denied back-to-back titles after his Japan Open Tennis Championships triumph last weekend as Tsitsipas struck 34 winners in a pulsating quarter-final in Shanghai, setting up a last-four contest with Medvedev.
Matteo Berrettini is up next for Zverev, who reflected on a remarkable end to the second set, when he was on the brink of a far more straightforward success.
Tsitsipas smacked the ball out of the court in a rage before Medvedev sealed the match in the 12th game of the second set. The world No. 4's win means he reaches his sixth consecutive final and eighth overall, an achievement that top-ranked Novak Djokovic called "amazing".
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.
"I don't know if I'm going to be able to beat him the next time or the time after that one, but I know there's going to be a time where I'm going to find opportunities and beat him". Medvedev and Berrettini are 23, Tsitsipas is 21 and Zverev is 22.
"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".
Medvedev has now seen off the 21-year-old - who defeated World No 1 Novak Djokovic on Friday - in all five of their matches.
"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.
"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 said Federer started to play better after his exchanges with the umpire. But he said that past meetings with Medvedev stood for nothing because the Russian has improved markedly since their last match, in 2018. Zverev may feel that, now that he has beaten Federer, the hard work is done, but the Italian has already proved his ability to handle the big occasion numerous times this year.
Stefanos Tsitsipas of Greece reacts as he plays against Daniil Medvedev of Russian Federation in their men's singles semifinals match at the Shanghai Masters tennis tournament at Qizhong Forest Sports City Tennis Center in Shanghai, China, Saturday, Oct. 12, 2019.
"He's definitely playing the best tennis of his life".