The tennis circuit is one of the few sports not to ban Russians following the war on Ukraine enabling the pair to take part in the first same-nation match at the finals since Roger Federer beat Stan Wawrinka in an all-Swiss semi-final in 2015.
They have to compete without their flag or country next to their names but some Ukranian payers have said they should be banned.
After the tie Rublev wrote "Peace, Peace, Peace, All we need," on a TV camera lens.
Rublev made a similar appeal in February, writing "No war please" on a TV camera lens shortly after Russia's invasion.
Rublev said his sixth career meeting with Medvedev reminded him of his encounter with the world No. 5 at the 2020 US Open quarter-finals, where he lost in straight sets, and the 25-year-old was determined to overcome his poor start.
Having shaken off the disappointment of squandering several chances to take Monday's opening set, Rublev hit back with 25 winners in the next two and held his nerve in the deciding tie-break to seal the victory on his fifth match point.
"I was thinking about the US Open, because when we played in the quarter-finals in 2020, I think I was 5-1 in a tie-break, also something like 6-2, but I was leading something similar in a tie-break," Rublev said.
"But when I lost that set, I couldn't play anymore, and I was thinking it can't happen (again) I have to change something. I have to keep playing, because if I win one set, even if I lose in three sets, it's still good, because here you have a group.
"So you have to fight for every point, every game, and I was able to win. The final tie-break, the rallies that we had there were crazy. The last rally, we had I don't know, 30 shots."
Rublev said he was cramping towards the end of the contest before winning with a 37-shot rally on match-point, after which he dropped to the floor in delight.
"I was thinking 'one more, one more. You have to keep playing'," Rublev, who also beat Medvedev in the Cincinnati semi-finals last year, said.
"For sure, he felt the same, 'so just keep playing if you have the chance, go for it'. In the end I was able to win."
Stefanos Tsitsipas and Novak Djokovic face off in the other Red Group match later on Monday.
With AP