Russian fifth seed Rublev claimed a 5-7, 6-1, 6-3 victory and will face either Jannik Sinner or Danish teenager Holger Rune in Sunday's final.
The 25-year-old is bidding to go one better than in 2021 when he lost the final to Stefanos Tsitsipas.
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 roared out following the restart with an immediate break.
He saw three match points come and go in the eighth game but wrapped it up with a hold to love.
