The Russian has previously lost in the final at Flushing Meadows and Melbourne but had never been past the opening round at Roland Garros prior to this run.
Four largely routine victories encouraged hopes of a triumph that would make Medvedev the world number one for the first time until he faced Tsitsipas, who had won only one of their prior seven meetings.
A second Tsitsipas success followed in striking fashion, the number two seed toppled 6-3 7-6 (7-3) 7-5. Alexander Zverev awaits Tsitsipas in the last four.
Tsitsipas was on the front foot from the outset and did not have to wait long for his first break and a 3-1 lead, one he could have extended further before serving out the opener in dominant fashion.
And a brutal break to love early in the second, with Medvedev struggling to keep up, further fastened the Greek's grip on the match.
But the sixth game belatedly brought some resistance that prompted Tsitsipas to send a wild forehand long, granting Medvedev momentum for the first time as he then stylishly held.
That progress seemed to slow with a change of ends and an apparent complaint about off-court noise in a supposedly empty stadium, yet Medvedev dug in again and then forged two break points, only to squander both.
And Tsitsipas' ability to outmanoeuvre his opponent came to the fore again in a one-sided tie-break.
A change of shirt did not alter Medvedev's fortunes for the better, as he worked hard to craft a break in the third but then immediately ceded his advantage.
Another distraction – this time the camera angle on the big screen – prompted a debate with the umpire, but Medvedev was by that stage serving to stay in the tournament and merely delayed the inevitable, confirmed when Tsitsipas blasted an awful underarm serve back past his forehand.