Taylor Fritz (25) showed great fight but was unable to match Alcaraz's level, the defending champion taking control with an instant break of serve in each set on the way to a 6-4 6-2 win.
In a high-quality clash between two players who reached the quarter-final without dropping a set, world number one Alcaraz never trailed and frustrated ninth seed Fritz with a potent mix of power, sublime shotmaking and relentless hustle.
"A little bit of nerves at the beginning of the match, it was new for me playing against him, never played him before," Alcaraz said after the match, which was originally scheduled for Wednesday but postponed due to rain.
"Of course I am really happy with the way that I started the match with no mistakes and with a lot of power. It was a key for me to break the serve at the beginning."
If Alcaraz lifts the title in Miami he would become the eighth man to win the Indian Wells and Miami tournaments back-to-back, a feat known as the 'Sunshine Double' given their locations in California and Florida.
Alcaraz next plays 10th seed Jannik Sinner (21), whom the Spaniard beat in the Indian Wells semi-finals to improve to 3-2 in head-to-head meetings with the Italian.
RYBAKINA ROLLS ON
Wimbledon champion Rybakina, who is seeking to become the fifth woman to win back up the Indian Wells title with the Miami crown, came through two rollercoaster sets and a couple of rain delays to beat Pegula 7-6(3) 6-4 in their semi-final.
Neither player was able to settle into their serve but Moscow-born Rybakina, who now represents Khazakhstan, came out on top in a tense tiebreak before edging the second set to record her 13th straight win.
"I was playing much better when I was down," Rybakina said on court after her first win over Pegula in three meetings. "First set was very tough. The tie-break could go both ways."
Rybakina's opponent in the final will be either twice Wimbledon champion Petra Kvitova (33), who beat Russia's Ekaterina Alexandrova (28) 6-4 3-6 6-3, or unseeded Romanian Sorana Cirstea.
Earlier on Thursday, Medvedev ended the dream run of American qualifier Christopher Eubanks (26) with an impressive 6-3 7-5 victory in a rain-interrupted match to reach the semi-finals of the tournament for the first time.
The fourth-seeded Russian trailed 3-2 in the first set before rain stopped play but when the match resumed 30 minutes later he was a man on a mission, winning the next five games and never trailed again.
Medvedev broke Eubanks for a fourth time to seal the win on his third match point when the American sent a forehand smash wide as the red-hot Russian prevailed 6-3 7-5 and has now won 22 of his past 23 matches.
"I didn't play my best before (the rain delay). The rain helped me go out and have more energy," said Medvedev. "It helped me and I only played better and better, apart from one bad game on my serve, but it happens."
Medvedev will next face fellow Russian Karen Khachanov (26), who advanced with a 6-3 6-2 win over Argentine Francisco Cerundolo (24).
