The Spaniard clinched a 6-3, 6-7 (7/9), 6-7 (0/7), 7-5, 6-3 victory in a tie which ended at 2:50 a.m. local time on Thursday.
At 5 hours and 15 minutes, it was the second-longest US Open match and surpassed the previous record for latest finish in New York of 2:26 a.m.
"I would say it was the best match I've played in my entire career," said world number four Alcaraz.
"At 5 hours 15 minutes, from the first ball to the last, there was immense quality from both Jannik and me."
He added: "Jannik and I will remember this for the rest of our lives."
Alcaraz is the youngest Grand Slam men's semi-finalist since Rafael Nadal at the 2005 French Open.
He is also the youngest US Open men's semi-finalist since Pete Sampras in 1990.
Although he is still chasing a maiden Grand Slam title, Alcaraz warned the clock maybe ticking on the dominance of Nadal, Novak Djokovic and Roger Federer who have 63 majors between them.
"As long as Rafa, Djokovic, Federer are there, they will be the best and the rivalry they have between them will always come first," he said.
"But today Jannik and I have shown that we are the present and that we also have a long career ahead of us. We are going to play many times together."
