Thiem will take on Alexander Zverev in his fourth slam final having lost twice to Rafael Nadal at Roland Garros and to Novak Djokovic at the Australian Open in January.
He very nearly won that one and he will surely believe this is finally his time after a 6-2 7-6 (7) 7-6 (5) victory over Russian Medvedev, who served for both the second and third sets but could not shake off Thiem.
Thiem said: "After the first set I think it was great tennis from both of us and I could have been two sets to one down. Tie-breaks are really mentally a tough thing. I don't like them at all really. I'm really, really happy to be through."
The pair had been comfortably the most impressive performers in the men's tournament through to the last four, with Medvedev having not dropped a set.
After coming so close to beating Nadal in his maiden final here last year, the 24-year-old knew what a huge opportunity this was, but Thiem's greater experience perhaps showed in better decision-making at the big moments.
Medvedev played the role of pantomime villain here 12 months ago and, had there been a crowd inside Arthur Ashe, they would surely have been jeering as the Russian lost his cool with umpire Damien Dumusois in the sixth game of the opening set.
Dumusois did not allow the third seed to challenge a serve that was clearly long and then gave Medvedev a warning for marching around to the other side of the net to show the umpire where the ball had landed.
The Russian could not let go of the incident and checked out of the set before heading off court for a bathroom break.
If Medvedev was hoping to break Thiem's rhythm, it worked, the Austrian playing a poor game to start the second set.
Medvedev will surely look back and wonder what might have happened had he taken any of numerous chances to level the match.
Having been two points away at 5-3 and 0-30 on the Thiem serve, he was broken serving for it and then missed five break points in the next game.
He had his chances in the tie-break, too, but too often a poor choice of shot came back to bite him, not least the supremely ill-advised drop shot he played at 7-7.
It was a huge steal for Thiem but he was beginning to struggle physically and called the trainer for treatment to his right Achilles.
Medvedev certainly looked the fresher during a third set that featured a passionate Thiem rant about his shoes after he slipped at a key moment.
It seemed to be Medvedev's for the taking but once again he could not seize the opportunity, with Thiem showing terrific resilience to break back for 5-4.
The second seed was in touching distance at 5-1 in the tie-break and, although Medvedev made a fight of it, Thiem made it across the finish line.