Russian Rublev fought back from 3-0 down to level the second set and then saved five match points, but the Spaniard ultimately prevailed to win his 11th straight match of the season.
"I know what I'm able to do every time that I step on court. For me it's great. Obviously, the way I'm approaching every match, I'm just really proud about it," said 22-year-old Alcaraz, who has been a finalist at the last four Grand Slams, winning three of them.
"I'm trying to be better at that... it's paying off. All the focus and attention. I'm just happy and proud about myself with how I'm getting better and getting mature I guess."
A struggling Rublev made 14 unforced backhand errors in the first set, but outwitted Alcaraz with precise forehands that nicked the baseline as both players broke the other twice each to go into a tiebreak.
Alcaraz held his nerve to go 6-3 up in the tiebreak as a frustrated Rublev repeatedly smashed the racket on his left knee, breaking a string. Seven-time Grand Slam winner Alcaraz then pretended to slice but landed a forehand down the sideline to win the first set.
Alcaraz broke Rublev twice to go 5-3 up in the second set and was serving for the match when the world number 14 saved three match points to break back.
But Alcaraz pushed to break again for victory in the next game, and finally converted his sixth match point when Rublev's backhand landed wide.
World number 16 Jakub Mensik will take on Arthur Fils in the second semi-final later in the day.
