The 21-year-old Spaniard beat incoming world number one Sinner 2-6, 6-3, 3-6, 6-4, 6-3 to become the youngest man to reach Grand Slam finals on all three surfaces.
"It's one of the toughest matches I've played, for sure," said Alcaraz.
"The toughest I've played in my short career have been against Jannik."
Alcaraz has won both of his two previous major finals -- at Wimbledon last year and the 2022 US Open.
He will play fourth seed Alexander Zverev or two-time Roland Garros runner-up Casper Ruud on Sunday, where a victory would see him head to the Australian Open next January seeking a career Grand Slam.
Both Alcaraz and Sinner, 22, arrived in Paris under an injury cloud, gradually finding their best level over the course of the tournament to set up a meeting billed as the match "everybody wants to see".
The ninth chapter of an enthralling rivalry that represents the future of men's tennis was the youngest Grand Slam semi-final pairing since Andy Murray beat Rafael Nadal at the 2008 US Open.
It was their first Grand Slam meeting since a spectacular five-set quarter-final two years ago in New York, and while perhaps not as exhilarating this one was no less gripping.
Alcaraz, who was hampered badly by cramp in last year's semi-final loss to Novak Djokovic, had said that playing Sinner was like running a marathon, and it was the Spaniard doing much of the chasing early.
Australian Open champion Sinner, who had lost just twice all year, broke three times as he dominated the first set, blending impenetrable defence with searing groundstrokes as he went on the attack.
Alcaraz belatedly spluttered into life though as Sinner struggled to maintain his sky-high standards from the opening set, allowing the Spaniard to scrap his way back into the match.
"You have to find the joy in suffering," said Alcaraz, admitting he had braced himself for a long match on what was a picture-perfect day in Paris.
"That's the key. Even more here on clay. Long rallies, four hour matches, five sets. You have to suffer. You have to enjoy it."
Lesson learned
Alcaraz briefly nosed in front at the beginning of the third set only for Sinner, dealing with cramp in his forearm, to wrest back the momentum and take the third set.
The tension wasn't just getting to Sinner, with Alcaraz trying to shake off his own bout of cramp.
"I learned from last year's match against Djokovic, when I was in the same position as today," said Alcaraz said.
"I know that, in this moment, you have to be calm, you have to keep going, because the cramp is going to go away. You have to stay there, fighting."
Both players stabilised on serve in the fourth, with not a single break point on offer until a sizzling Alcaraz backhand brought about a set point.
He didn't flinch and sent the match to a decider with a winner into the open court.
Alcaraz's approach to grind Sinner down coupled with timely shotmaking allowed him to strike the critical blow in the second game of the fifth set.
"The fourth and fifth was great tennis," said Alcaraz. "I waited for my moment until I took it."
Sinner, while visibly flagging more than his re-energised rival, did not go down without a fight, but Alcaraz finally put him away after four hours of another absorbing showdown.
"It was a great match," said Sinner, who will replace Djokovic at the top of the rankings next week.
"For sure the sets he won he played better in the important points, no? I think that was the key."