Neither man was broken in the fifth set. Shelton, who had lost all three of his previous meetings with him, now plays Frances Tiafoe in an all-American semifinal, the third at a Grand Slam this century.
The American won against Greek Stefanos Tsitsipas (6-2, 6-3, 6-4), Canadian Denis Shapovalov (7-6 (3), 6-7 (5), 6-3, 6-4), Pole Hubert Hurkacz (6-3, 5-7, 7-6 (3), 7-5) and Dutchman Tallon Griekspoor (1-6, 6-1, 7-6 (3), 6-2) ahead of his victory.
Earlier in the tournament, Alcaraz, ranked No 3, beat American Tommy Paul, the No 20 seed (6-4, 6-3, 6-4), Chinese Yibing Wu (6-3, 6-4, 6-1), Portuguese Jaime Faria (4-6, 6-0, 6-3, 6-2) and Russian Roman Safiullin (6-4, 6-4, 6-4).