Top seed Alcaraz eclipsed Sinner 7-6(4) 6-3 in a thrilling encounter that was reminiscent of their epic clash at last year's US Open.
An early break allowed Alcaraz to gain a 4-2 advantage, however, Sinner rattled off three games in a row en route to taking a 6-5 lead.
The Italian had an opportunity to take the first set, but Alcaraz managed to fend off the set point and force a tiebreak.
That effort signaled a change in momentum for Alcaraz, who claimed the tiebreak and cruised to victory in the second set, wrapping up the match in an hour and 52 minutes.
"I'm really happy with the performance today," said Alcaraz, as per atptour.com.
"I'm really happy to get through this great match. Jannik obviously is a really great player with great shots.
"I would say we're going to have a great rivalry over the years. We are playing in the best tournaments in the world. It's not over here. We are going to play a lot of great matches. All I can say is I'm really happy with my first final here in Indian Wells."
Alcaraz will face Russia's Daniil Medvedev in the final, after the world number six earlier overcame Frances Tiafoe in a grueling back-and-forth affair.
American Tiafoe saved seven match points in a spirited ending to the first semi-final but eventually fell to a 7-5 7-6(4) defeat as Medvedev made it 19 victories in a row.
A win against Medvedev would propel Alcaraz back to world number one after injury brought a premature end to his previous reign on top.