Rune fights back to set up final against Rublev in Monte Carlo
The 19-year-old claimed a 1-6, 7-5, 7-5 win under floodlights after a rain-affected day in the principality.
Russian fifth seed Rublev saw off Taylor Fritz 5-7, 6-1, 6-3 in the first semi-final.
Rune continued his meteoric rise in the sport with another statement victory, having climbed into the world's top 10 this season after a breakthrough 2022 which he capped off with the Paris Masters title, beating Novak Djokovic in the final.
"It was quite unbelievable," Rune said. "Jannik started firing, hitting a lot of winners and he has been in good form the past few months.
"I had to dig deep and find solutions, which I did well. It was fun to play like this."
Sinner dominated the opening set but was 3-0 down in the second when the players were forced off by the inclement weather.
Rune lost that advantage after the resumption but continued to put pressure on the Sinner serve and levelled the match in the 12th game on his fourth set point.
World number nine Rune saw five break points come and go in the third set as it stayed on serve for 11 games.
But he made the decisive move and secured a place in his second Masters final on his first match point as Sinner dumped a forehand into the net.
Rublev reaches second final
Earlier, Rublev also battled back from a set down to beat big-serving American Fritz and reach his second Monte Carlo final.
The 25-year-old is bidding to go one better than in 2021 when he lost the final to Stefanos Tsitsipas.
"It was really tough, especially against Taylor," Rublev said after his first win in his last four meetings with Fritz.
"It was tough mentally to play against him because I was thinking if I would have chances. I started really well and then I was up a break and then he broke me back, but I knew I would have chances.
"In the end we had a great match and I am pleased with the win."
Fritz is still waiting to reach a maiden ATP final on clay despite an excellent week.
Both players struggled on serve in a long opening set, but eighth seed Fritz grabbed the lead with a break in the 12th game.
Rublev raced through the second set to force a decider, which was halted by a long rain delay with the world number six 3-2 ahead on serve.
Rublev further upped his level following the restart with an immediate break.
He saw three match points pass him by in the eighth game but wrapped it up with a hold to love.
Rublev will be playing in his second final of the season, after losing to Daniil Medvedev in Rotterdam in March.