The Australian Open champion, Roger Federer, was ahead 2-1 in the first set following a three-hour rain delay.
After play resumed, the Italians won the first game, but the Spaniards Alcaraz rallied for victories of 1-6, 6-3, and 6-2.
Additionally, Russian Medvedev overcame a set down to defeat American Tommy Paul 1-6, 7-6, (7-3) 6-2 in his semifinal match.
The championship match will be a rematch of the one Alcaraz won handily the previous year.
“It is amazing for me to be able to end something like this,” 20-year-old world number two Alcaraz said of breaking Sinner’s run.
“I think that is a really important part of this game; I stayed mentally strong.”
“I am really happy with what I have done in this kind of match, a set-down against someone who is playing an unbelievable game.“I think it worked very, very well,” the player said after making minor adjustments to both style and game.
In the third set, Sinner committed eight of his fifteen unforced errors, while Alcaraz committed just two in the decider.
The 22-year-old world number three Sinner said, “It is definitely not the ending that I wanted, but playing against him is always tough.”
“I made an effort to play well, which I did, particularly in the opening set.
Subsequently, I committed several errors. The flow of momentum shifted. He performed at a higher level.”
When he faces Medvedev, Alcaraz will be looking to win his first championship since Wimbledon of last year.
“I am going to do everything in my power to turn this around, to play better, to play stronger, more on the lines, hit more aces, and stuff like that because I know what happened last year,” the 28-year-old Russian player declared.
“Hopefully, I can pull it off.”