'I'm a bull': Alcaraz marks 20th birthday by reaching Madrid final
The world number two was at his best to defeat the Croatian, who pushed him hard but ultimately came up short against the Spaniard.
"The truth is it's incredible to turn 20 with you, every year it's my birthday here," said Alcaraz.
"I turned 18 against Rafa (Nadal), my 19th birthday I won an incredible match against (Cameron) Norrie, and 20 here, getting to the final, each year is so special."
Alcaraz, reaching his fourth Masters 1000 final, broke for a 3-2 lead in a tight first set and served it out.
The US Open champion broke for 2-1 in the second set and after world number 20 Coric immediately hit back, did so again for a 3-2 lead, which he consolidated.
Alcaraz sealed the match with another break when Coric went long, ensuring he reached the final only dropping one set en route, against Emil Ruusuvuori.
"The truth is that Coric is such a tough player, you could see that during the while match, but especially at the start of the first set," said Alcaraz.
"It was 2-2 after almost 40 minutes, really long rallies, high intensity."
Alcaraz said he called upon some of the inner motivation which helped him triumph at Flushing Meadows in New York last year when he captured his maiden Slam.
"There was a moment when I repeated what I repeated at the US Open, that I'm a bull, and that I could do it, and it helped me."
The top seed was able to celebrate with a birthday cake, offered to him by the tournament organisers after his victory.
Later Friday lucky loser Jan-Lennard Struff faces Aslan Karatsev in the other semi-final - the same opponent who knocked him out in qualifying.
The women's final between the world number one Iga Swiatek and number two, Aryna Sabalenka, takes place on Saturday.