Sixth seed Tsitsipas had a record of played five, lost five against Medvedev, who was this year's US Open runner-up having enjoyed a stellar breakthrough season.
But the 21-year-old from Greece found London's 02 Arena to his liking as he ground out a 7-6 (5) 6-4 victory.
Russian Medvedev, 23, has won more matches than any other player this year, his total of 59 victories being five more than Novak Djokovic has managed.
HUGE win for @StefTsitsipas 👏
— ATP Tour (@atptour) November 11, 2019
But he could not manufacture a single break point against the dogged Tsitsipas, who secured the only break of the match at 5-4 in the second set before serving out.
Tsitsipas said: "It was one of the toughest, most important victories of my career so far.
"I gave myself a big boost, I kept believing, kept fighting, believing in myself, and that last game was one of the toughest.
"It's such a relief. It's not easy coming in knowing you lost five before, but I made a deal with myself to keep trying.
"I had great support, there are Greek flags everywhere, it feels like I'm playing in Athens. I had goosebumps."