Medvedev, who has repeatedly said he feels more comfortable on hardcourts, continued his stellar run on clay with a 7-5 7-5 win over 2021 French Open runner-up Stefanos Tsitsipas (24) and will aim to capture his fifth crown of the year in Sunday's final.
Earlier, French and US Open runner-up Ruud won a tight first set with 22 winners, including 11 on his forehand, and looked on course for a spot in the final after grabbing the first break of the match in the second set for a 4-2 lead.
"I told myself at this moment I had nothing to lose, he's probably going to win the match," Denmark's Rune said.
"So I told myself to play free and enjoy myself as it would probably be my last set here."
Rune took a medical timeout for a minor shoulder problem and that looked to throw Estoril champion Ruud off his game as the 24-year-old Norwegian surrendered his serve twice to get dragged into a deciding set.
A double-fault gifted Rune a break and a 3-1 lead in the final set and he never looked back as he sealed a first victory over Ruud in their fifth meeting.
"I really played some of my best tennis," said Rune, who beat world number one Novak Djokovic (36) in the quarter-finals.
"Especially in the matches against Novak and Casper. Such difficult players to play against. I had to find my best tennis and I actually didn't find it today until the end. That's why I turned it around."
Third seed Medvedev broke in the opening game of his semi-final but the Russian dropped serve before rain stopped play. The players returned after nearly three hours for one game before the match was halted again.
Back after another frustrating delay, Tsitsipas squandered a 40-0 lead to allow Medvedev to go up 6-5 and eventually take the advantage in the clash.
After the players traded breaks in the second set, Medvedev got in front again after the 11th game and closed out the win on serve and celebrated reaching his first Masters final on clay with an impromptu dance.
"It's like being in the club completely drunk," Medvedev said of his jig. "I enjoyed playing today. It was very tough with the rain delays.
"I warmed up six or seven times. Sometimes it throws you off and you can be angry with the situation, but today I don't know why but I was just laughing."
In the women's final, Wimbledon champion Elena Rybakina (23) meets Ukraine's Anhelina Kalinina (26).
