Australian Open champion Sinner has been the hottest player on tour this year and looked poised to run away with the match when the Spaniard's forehand went long to end the 34-minute opening set, which was halted by a three-hour rain delay.
Alcaraz would finally break serve with a powerful forehand that set up a put-away volley for a 3-1 second set lead and hit a drop shot even the speedy Sinner did not try to race down to force a decider between the young rivals.
With Sinner serving in the third set, the Italian dove to keep a ball in play on break point near the net, his hands scraping along the gritty Indian Wells hard court.
Alcaraz's athletic volley secured the break and Sinner appeared to be bothered by his left hand after the exchange.
Alcaraz went up a double break and 4-1 on a forehand wide by a suddenly error-prone Sinner and sealed the win with a crosscourt forehand winner to keep Sinner from taking his world number two ranking and denying him a 20th consecutive win going back to last year.
"I stayed strong mentally and that's very important," Alcaraz said.
"I had to run more, defend better than I did in the first set. Put more balls in. Stay strong on the court."
Alcaraz will face Daniil Medvedev in Sunday's final as he did in 2023.
The Russian eked out a similar comeback win against Tommy Paul, who was quick off the blocks, dropping just one game in the opening set before Medvedev bounced back.
Paul saved two set points to force a tie-break in the second set but Medvedev won five straight points to draw level with him.
Paul was broken from 40-0 in the first game of the third set, which was pretty much a one-sided affair as Medvedev closed out the match to stay on course to avenge his loss to Alcaraz in last year's final.
"He played an unbelievable first set," Medvedev said of his opponent.
"So I was like, OK, if I want to win I just have to try to do a little bit better to find the shot that's going to make him in trouble. I found some, especially on his serve."
