Alcaraz defeated Djokovic 6-7 (5-7), 7-5, 7-6 (7-5) in the semifinals after a lack of 3.38 on the gravel.
Alcaraz, who turned 19 on Thursday, had a match ball at 5-4 in the third set but Djokovid saved himself with a serveess.
The Serb saved another match ball at 4-6 in the tiebreak but Alcaraz hit a heavy straight forehand and evoked ecstasy on the packed stands in Madrid.
He fired a ball into the air and then clenched his fist at the crowd and went forward to thank Djokovic at the net.
Djokovic smiled happily and hugged Alcaraz, world number nine on the rankings.