Shortly after Alcaraz wove his magic to dismantle 24-time Grand Slam champion Novak Djokovic at Arthur Ashe Stadium, the usually machine-like Sinner misfired at times but prevailed to ensure a third successive major final with the Spaniard.
The hard-fought victory makes Sinner only the fourth man in the professional era that began in 1968 to reach all four Grand Slam finals in a single season, joining Djokovic, Rod Laver and Roger Federer.
"Amazing season. The Grand Slams are the most important tournaments we have, and finding myself again in another final, especially the last one this season, with an amazing crowd... It doesn't get any better," Sinner said.
"Felix and I played in the last tournament (in Cincinnati). He's a completely different player. He was serving much better, hitting every shot much better, so it was a tough match, but I'm obviously very happy.
"I saw he was injured at some point, so hopefully it's nothing bad. I wish him only the best. He's an amazing player and an amazing person, so it's always nice to share some nice matches with him."
The Italian world number one faced brief resistance in the fifth game of the contest but dialled up the intensity to hold and wrapped up the lopsided opening set when Auger-Aliassime sent a backhand wide.
Auger-Aliassime settled his nerves in his second New York semi-final, breaking for a 5-3 lead in the next set en route to levelling the match, before going toe-to-toe with Sinner in the third set, only for the momentum to shift again.
Sinner, who took a medical timeout for an unspecified issue, found his groove to close out the third set, staving off a strong challenge from his reinvigorated Canadian opponent with some clutch serving in the next set to advance.
He told reporters afterwards he felt twitching in his stomach while serving at 4-3 in the second set, but played down concerns about his fitness.
"After the treatment, I was feeling much better," he said.
"At some point, I didn't feel anything anymore. I was serving back at normal pace, so it was all good.
"Nothing to worry about. But I preferred to go off court because it's on a different spot."
The victory set up a mouth-watering encounter with second seed Alcaraz, who saved three matchpoints in their French Open final meeting in June to retain his title before surrendering his Wimbledon crown to the Italian in July.
Sinner looked ahead to their major trilogy meeting, which will take place on Sunday, three years after the pair duelled in the New York quarter-finals in an entertaining five-setter that Alcaraz won before going on to lift the sterling silver trophy.
"I feel our rivalry started here, playing an amazing match," Sinner said.
"We're two different players now, different confidence too, so let's see what's coming. We've played quite a lot this year, so we know each other very well. In any case, it has been an amazing tournament, an amazing feeling to play in front of you.
"I'm looking forward to doing it again."