The match broke the record for the latest ever finish at Flushing Meadows, with the epic encounter ending at 3.33am Wednesday.
Alcaraz won a tight first set and later levelled the clash at two sets apiece despite struggling with unforced errors, but he was unable to get over the finish line as Shelton raised his level when it mattered to prevail.
The Spaniard had his 18-match winning streak in Grand Slam tournaments ended in a duel that lasted four hours, 28 minutes.
Shelton will next play No. 11 seed Frances Tiafoe, who kept coming back until he had reached his third US Open semifinal, beating Alex Michelsen 5-7, 3-6, 7-5, 6-3, 7-6 (10-6) on Tuesday.
The US is guaranteed to have a man in Sunday’s final as it seeks its first men’s major title since Andy Roddick in 2003. (Agencies)