Sinner ended Alcaraz's winning streak at 10 matches, the Italian's powerfully steady baseline game wearing down the Spaniard, who appeared to be cramping early in the decisive third set while he also dealing with an apparent finger injury.
Alcatraz will now lose the No.1 ranking to Novak Djokovic.
Sinner, the 21-year-old who made the Miami Open final last year but hasn't been past the quarterfinals of a major, will face fourth-seeded Daniil Medvedev of Russia in the championship match Sunday. Medvedev has beaten Sinner in all five meetings.
Alcaraz had been so dominant he hadn't lost a set since February before Sinner rallied in the Miami humidity.
The pair had met in the Indian Wells semifinals but this Sinner overturned that straight-sets victory and ended Alcaraz's hopes of becoming the first man since Roger Federer in 2017 to win the Sunshine Double.
Alcaraz prevailed in the first set on Friday but it took plenty out of him, the Spaniard stretching noticeably during the third set and trying to stave off cramps.
Sinner stunned Alcaraz in the ninth game of the second set, breaking him at love to go up 5-4 and then closing it out.
An ATP trainer came out to attend to Alcaraz midway through the second set, examining one of his fingers before the cramps set in.
Alcaraz said the issues began after taking a five-minute bathroom break after losing the second set.
"When you stop for five minutes, I know it wasn't good for me,'' said Alcaraz, who committed nine double faults and 27 unforced errors. "I struggled with some problems.''
Medvedev beat fellow Russian Karen Khachanov 7-6 (7-5) 3-6 6-3 on the same day Wimbledon announced Russians will be allowed back into the tournament.
Medvedev has now won 23 of his last 24 matches — the lone loss to Alcaraz — and is in his fifth straight final.
"Really happy to be through a very tough match," Medvedev said in his on-court interview.
He was tested early before taking the opening set in a tiebreak, Khachanov then winning 12 of the first 15 points of the second set and eventually went on to level the clash.
But Medvedev, who entered the match having not dropped a set in Miami, showed his resolve and patience to race out to a 4-1 lead and held on to his advantage.
"In the second set I played one bad game, it was enough for him to win," Medvedev told Amazon Prime.
"Third set he had one break point (in the) first game, plays one bad game and it was enough for me to win."
With PA.
