The Bulgarian entering the Miami semifinals for the first time, Dimitrov has reached the last four at eight of the nine ATP Masters 1000 tournaments.
The 20-year-old Alcaraz was aiming to match his Miami semi-final result from last year and become the first player to reach three consecutive semis in south Florida since Novak Djokovic in 2014-16.
The Bulgarian will next play against fourth seed German Alexander Zverev in what will be his fourth semifinal of the season.
Dimitrov will return to the Top 10 for the first time since 2018 if he makes the Miami final.
