The Spaniard's best Grand Slam run came during the 2021 US Open where he earned his place in the quarter-finals.
Alcaraz is the youngest Miami men's champion in the event's 37-year history, as well as the third-youngest ATP Masters 1000 champion overall.
Iga Swiatek defeated Naomi Osaka in the Miami Open final on Saturday to win her third WTA 1000 title in a row.
Swiatek became the youngest woman in history to achieve the Sunshine Double, winning the Indian Wells and Miami Open in the same season.
Alcaraz controlled the second tie-break with the help of some untimely Hurkacz errors after erasing two break points at 5-all.
Swiatek beat No.16 seed Pegula, the last American standing in singles at the Miami Open, in an hour and 48 minutes.
Alcaraz was two points away from losing at 4-5, 15/30, and 5/3 in the tie-break, where he trailed by a mini-break on both occasions.
Caroline Wozniacki, Victoria Azarenka, and Jelena Ostapenko are the only other players to have made four or more WTA 1000 semifinals before turning 21.
Zverev did make an outstanding comeback in the second set after losing the first, but his opponent on the day was just too good.
Swiatek still has a chance to complete the "Sunshine Double" by winning Indian Wells and Miami in the same season.