Both players traded several breaks of serve in a breathless first set that tipped Sinner's way when he cracked a blistering return off the Spaniard's second serve to take the all-important tie-break.
But Alcaraz - the tournament favourite in Novak Djokovic's absence - then fell apart, gifting Sinner three service games before crowning an error-laden second set with a tame backhand into the net to give the world number seven a 7-6 (7/4), 6-1 victory.
Sinner and Medvedev will go toe-to-toe for the trophy on Wednesday.
Earlier, Medvedev hailed his "perfect" serve as he eased into the men's final with a 6-4, 6-3 win over Alexander Zverev.
The semi-final got off to a close-fought start but Medvedev then notched a crucial break of serve and managed to see out the first set.
It was a similar story in the second set, with the Russian breaking for 5-3 and serving out the match with a pair of fierce aces.
"Today was a perfect service match. I don't think there was one bad thing I can say about my serve," Medvedev said at a post-match news conference.
"I think the fact that the play was faster - the faster the court is, the easier you can hit aces... (and) the easier you feel when stepping into the serve," the 27-year-old said.
"Today I was going faster and I was really not thinking much about anything, just serving."
