The Russian, who came from two sets down to see off Felix Auger-Aliassime in the last round, triumphed 7-6 (7-5) 4-6 6-4 6-1 to set up a final with Rafael Nadal.
The US Open champion improved his head-to-head record with Tsitsipas to 7-2 in a contest where tempers frayed, mostly on Medvedev's side of the net.
He accused Tsitsipas' father of coaching from the sidelines and received a warning for his persistent complaining, but the second seed also managed to channel his aggression into a stellar performance.
The first set went the distance after Tsitsipas, who employed a bold approach in taking the match to Medvedev, fended off three break points when serving at 4-4.
Medvedev was 4-2 down in the tie-break but dug deep to claim it, underlining his mental toughness when backed into a corner.
Tsitsipas maintained his positive attitude and broke in the opening game of the second set, only to surrender that advantage in a sloppy sixth game as his accuracy abandoned him.
It was Medvedev who lost his way at 4-4, though, two double faults and a terribly skewed forehand seeing him lose serve, with Tsitsipas capitalising to seal the set.
Medvedev lost his cool with the umpire, bemoaning supposed coaching from Tsitsipas' father, but it only seemed to fuel him.
With Tsitsipas serving to stay in the set, Medvedev showed his range with a drop-shot winner and double-handed forehand bullet en route to a timely break to reclaim the lead.
And he was at his imperious best in the fourth, producing an array of stunning passing shots as Tsitsipas simply ran out of answers.
Medvedev now has the chance to go one better than last year, when he lost in the final to Novak Djokovic.