The Spaniard is bidding to win back-to-back titles in his homeland for the second year in a row after successfully defending the title in Barcelona last month.
Croatian Coric put up a good fight on Friday, with the first set in particular full of gruelling all-court rallies, but ultimately Alcaraz was too good and he claimed a 6-4 6-3 victory.
After the pair had shaken hands, the home hero was presented with an enormous birthday cake while the crowd sang happy birthday.
"It means a lot to me, playing a final again here in Madrid," said Alcaraz. "It's such a special place for me and I have great memories since I came here to play under-12s. Of course, last year was amazing.
"Turning 20 like that is special, so I will enjoy the final here and of course I will try to make all of Spain happy."
Alcaraz's latest win came as Rafael Nadal said he would miss the Italian Open in Rome next week as he continues to recover from a hip injury.
The younger Spaniard is rapidly establishing himself as the French Open favourite.
Novak Djokovic missed Madrid with an elbow problem and, if he wins the title this weekend, Alcaraz will only need to play a match in Rome to ensure he returns to world number one.
9°C