Alcaraz had his 18-match winning streak in grand slam tournaments ended in a clash that lasted four hours 28 minutes.
Shelton will play 11th seed Frances Tiafoe, who reached his third US Open semi-final by beating fellow American Alex Michelsen 5-7 3-6 7-5 6-3 7-6 (10-6) earlier on Tuesday (Wednesday AEST).
The US are guaranteed a player in Sunday's decider as they seek a first men's major title winner since Andy Roddick in 2003.
Alcaraz had played in the previous latest finish at Flushing Meadows when he outlasted Jannik Sinner in a match that finished at 2.50am in the 2022 quarter-finals, en route to his first slam title at 19.
Thousands of fans stayed to the end and Shelton benefited from a home-crowd boost, even against the popular Alcaraz, with fans in Arthur Ashe Stadium chanting his name along with "USA! USA!"
"It's incredible," Shelton said.
"I always say that this is the greatest sports city in the world, I say that this is the greatest stadium in the world. I'm just hoping that my best friend and my sister over there don't have to be at work at 6am in three hours."
Shelton reached his third major semi-final, having gotten to the 2023 US Open final four and 2025 Australian Open.
He seized control by winning nine straight games from early in the second set until he had a 3-0 lead in the third. But Alcaraz, in his first tournament since April after returning from a right wrist injury, battled back even as he vomited before the start of the final set.
He won the Australian Open to start this year, not long before his injury.
Shelton eventually finished it off with a 235km/h serve his opponent couldn't get back.
Tiafoe was the tennis equivalent of the relentless Terminator, he simply kept coming back until he had triumphed after four hours 38 minutes.
He then jogged over to the other side of the net, where the 22-year-old Michelsen cried on his shoulder after a devastating end to his first career major quarter-final.
"I'm going to enjoy this one, though. Let's go!" 11th-seeded Tiafoe, who also reached the final four at Flushing Meadows in 2022 and 2024, told the crowd.
Tiafoe lost to Alcaraz in 2022, when the Spaniard won the first of his seven grand slam titles, and to compatriot Taylor Fritz two years later.
It certainly didn't appear Tiafoe would be contesting the title match this time, after Michelsen continued his dominant run through his breakout tournament.
He was the only man who hadn't dropped a set and he served for the match with a 5-4 lead in the third.
Tiafoe joined Andre Agassi as the only American men to reach three US Open semis this century and will return to the top 10 for the first time in three years in the next rankings.
Michelsen, ranked 46th, fell to 0-6 in matches that go to a fifth set.
