The Greek star traded blows with the world number one for two and half hours on the hard court coliseum of the Linder Family Tennis Centre in Cincinnati, winning 7-6(3), 3-6, 6-3.
The opening set was on a knife edge, with Tsitsipas saving a set point in the tiebreaker before breaking back to seal the set. Medvedev bounced back strongly, racing to a 5-0 lead before levelling the match at one set apiece.
The final set saw Tsitsipas lean heavily on more net play - which he rushed to on no less than 36 occasions - to upset Medvedev's rhythm. The Russian's first serve percentage dropped to just 50% as Tsitsipas took advantage of the only break point and calmly served out the match to reach his fifth final of the year.
"There were some difficult shots I had to play a bit more," said the 24-year-old after the match.
"A few short balls I really took advantage of and came in. A lot of courageous serve and volleys, approaches to the net that definitely gave me that great win today."
The win sets up a final against the talented Borna Coric, who eased past British hopeful Cameron Norrie 6-3, 6-4 earlier in the day.
The Croatian made up for his woeful 43% first serve percentage with a superlative groundgame from the back of the court, crushing 22 winners.
"At the beginning, I was not there, I was not feeling the ball very well," admitted Coric.
"Then I did find my rhythm. I started to serve better, I started to play much better and I think that was the key to the match."
Coric and Tstitsipas have only met twice before on court, with the Greek winning the first match after Croric was first to retire in the opening set, then Coric outlasting Tstitsipas in a five-set thriller at the US Open in 2020.