The American eighth seed recovered from losing the opening set to beat world No. 3 Alcaraz 6-7(5), 6-1, 6-3, 1-6, 7-6(10-7) in a gruelling contest that lasted four hours and 28 minutes.
The match, played at Arthur Ashe Stadium, finished at 3:33 a.m. local time, making it the latest-finishing match in US Open history. Shelton's victory also ended Alcaraz's 18-match Grand Slam winning streak.
Alcaraz strikes first before Shelton responds
Alcaraz, who returned to competitive action in New York after almost five months away because of a wrist problem, edged a tightly contested opening set in a tiebreak.
Shelton responded emphatically in the second set, racing to a 6-1 victory before taking the third set 6-3 to move within one set of a major upset.
The two-time US Open champion refused to surrender, however, with Alcaraz winning the fourth set 6-1 to force a deciding set.
Neither player could break decisively in the fifth, sending the contest into a match tiebreak. Shelton held his nerve in the crucial moments, eventually winning 10-7 to complete a remarkable victory.
Shelton ends Alcaraz's American Grand Slam record
The victory was particularly significant because Alcaraz had entered the match with a 13-0 record against American opponents at Grand Slam tournaments.
Shelton also claimed his first victory over a top-three opponent after previously holding an 0-17 record in such matches.
The 23-year-old American will now face compatriot Frances Tiafoe in the semi-finals, guaranteeing an all-American contest for a place in the US Open final. Tiafoe reached the last four after coming from behind to defeat Alex Michelsen.
For Shelton, the victory represents his second US Open semi-final, having previously reached the last four at Flushing Meadows in 2023.
Alcaraz, meanwhile, leaves New York without the opportunity to defend his 2025 title, although his return to competitive tennis after his lengthy injury absence ended with a memorable quarter-final battle.