Alcaraz, 21, will play fourth seed Alexander Zverev or two-time Roland Garros runner-up Casper Ruud on Sunday after becoming 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. I hope to play many, many more like this."
"You have to find the joy in suffering," the Spaniard added.
Alcaraz has won both of his two previous major finals - at Wimbledon last year and the 2022 US Open. Victory on Sunday would see him head to the Australian Open next January seeking a career Grand Slam.
Both Alcaraz and Sinner 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 destined to shape the future of the sport 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.
Sinner pinned Alcaraz on the back foot straight away as he broke in the very first game, blending impenetrable defence with searing groundstrokes as he went on the attack.
After holding with ease the Australian Open champion belted a forehand winner for another break opportunity in the third game, sweeping 3-0 in front following an Alcaraz miscue.
Alcaraz finally got on the board in the fifth game before retrieving a break, but he handed it right back and Sinner bagged the first set when the Spaniard dumped a drop-shot into the net.
Sinner began the second set in identical fashion, earning another break after a loose Alcaraz service game and consolidating for a 2-0 edge on a picture-perfect day in Paris.
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Sinner's level drops
Alcaraz belatedly spluttered into life though as Sinner struggled to maintain his sky-high standards from the opening set and presented his rival three break points with a double-fault.
A brilliant cross-court winner hauled Alcaraz back on serve, with the Spaniard soon accelerating 5-2 ahead following another break as Sinner sprayed his forehand wide.
Sinner temporarily slowed the Alcaraz charge, ending his five-game winning stretch, but the third seed levelled up the match the next game.
The early onslaught from Sinner felt a distant memory as Alcaraz pounced to break for a 2-1 lead in the third set, flicking a sublime backhand passing shot beyond a powerless Sinner.
Yet the momentum was quickly back with Sinner.
He ripped a blistering one-two combination of forehands to get back on serve and then resisted four break points in a lengthy fifth game before holding for 3-2.
Sinner received a massage from the physio for apparent cramp in his right forearm, but he brushed off any physical issue as he hammered a backhand return past Alcaraz to break again.
A tame Alcaraz forehand into the net handed Sinner the third set. A sense of calmness enveloped 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.
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 seismic showdown.