WATCH the ATP Tour LIVE on beIN SPORTS | Sign up to beIN CONNECT to take advantage of our 7-day free trial
Medvedev had never previously won a match in Rome and had made clear his dislike of clay but the Russian will be seeded second at Roland Garros and has put himself right in the mix for what could be an open tournament.
Rune is at his best on the surface and had knocked out Djokovic and Casper Ruud to reach the final but Medvedev twice came back from a break down to clinch a 7-5 7-5 victory.
Medvedev claimed the first break of a tight first set in the 12th game and won the final four games of the match after Rune had led 5-3.
Speaking on Amazon Prime Video, Medvedev said: “I always want to believe in myself and I always try to do my best, I want to win the biggest tournaments.
“At the same time, I honestly didn’t believe much I can win a Masters 1000 on clay in my career because usually I hated it, I hated playing on it, nothing was working.
“Before this tournament, already in Madrid and Monte-Carlo I was feeling not too bad. Coming here, I felt amazing in practice. But then you need to play the toughest opponents in the world and I’m really happy that I managed to do it and prove to myself and everybody that I’m capable of doing it.”
Medvedev is still not completely won over by clay, though, adding: “(It’s a) friendship. I don’t think I love it, I love hard courts, my only love – in tennis. But I definitely like clay courts much more now.”
Rune will climb to a new career high ranking of six, and the 20-year-old told reporters in the Italian capital: “I think I was very nervous stepping into the match.
“Obviously I came through from a great match yesterday. Maybe I put too many expectations on myself, even though I told myself not to. He played great. He played really solid from the back of the court.
“Paris is the main goal of the clay season. I think I had the matches that I needed to be as well prepared as possible. Now it is the last small things I want to do better the next time I play in these big matches.”
Meanwhile, Britain’s Jack Draper returned from injury with a 6-2 6-3 victory over Alexandre Muller in the first round of the ATP Tour event in Lyon.
Draper has played only one tournament since March because of an abdominal problem.