Defending champion Alcaraz moved to within one win of a potential dream final with Novak Djokovic with an emphatic straight sets victory over German 12th Alexander Zverev.
Zverev had emerged as a dark horse after a marathon five-set win over Italy's sixth seed Jannik Sinner on Monday.
But the German's hopes of extending his stay in New York were obliterated by a devastatingly clinical performance from Alcaraz, who completed a 6-3, 6-2, 6-4 win in 2hr 30min on the Arthur Ashe Stadium court.
The victory leaves the 20-year-old Alcaraz firmly on course for another final showdown with 23-time Grand Slam champion Djokovic after their Wimbledon classic in July.
Djokovic faces unseeded American Ben Shelton in Friday's other semifinal.
"I'm feeling really comfortable playing on this court, playing in New York," said Alcaraz, who will face Russian third seed Medvedev in the semifinals on Friday.
"I'm feeling strong. I think I'm ready for a great battle against Medvedev," added Alcaraz, who has dropped just one set en route to the last four.
Medvedev had earlier secured his place in the semifinals with a 6-4, 6-3, 6-4 victory over compatriot Andrey Rublev in punishing, furnace-like conditions that the Russian said endangered players.
New York has been sweltering in a heatwave this week, with high humidity and temperatures at Flushing Meadows on Wednesday hitting 35 degrees Celsius (95 Fahrenheit).
Tournament organisers confirmed that extreme heat measures were in effect for the quarterfinal – but Medvedev was clearly unimpressed.
At one point during the third set, the 2021 US Open champion muttered to a nearby TV camera "one player is going to die and they're going to see" as he grabbed a towel.
"The conditions were brutal. The only good thing is that both players suffer, so it's tough for both of us," Medvedev said after his victory in 2hr 48min.
"At the end of the first set I kind of couldn't see the ball anymore. I kind of just played with sensations."
Both Medvedev and Rublev attempted to cool down during changeovers by wrapping towels packed with ice around them, while Medvedev could be seen puffing from an inhaler.
ZHENG LEFT IN SHADE
Wednesday's play got under way earlier in blazing sunshine on Arthur Ashe, where China's Zheng Qinwen struggled before being overwhelmed by second seed Aryna Sabalenka 6-1, 6-4.
Zheng said the partially closed roof on Arthur Ashe – a move designed to protect spectators from the sun – had caused her problems, making it hard to focus on the ball with shadows darkening part of the court.
"I hate that different half-shadow, half-sun," Zheng said. "Because I feel that's also bad, I mean, my eyes."
Sabalenka however had no difficulty in adapting, with the Belarusian dominating her opponent with a powerful service game that sends her into a last four meeting with 17th seeded American Madison Keys.
Sabalenka was assured of replacing Iga Swiatek at the top of the women's rankings after the Polish No 1 crashed out of the US Open on Sunday.
However Sabalenka said she is not thinking about her new-found status as the world's top player just yet.
"Of course I'm happy ... it's incredible for me and my family.
"But I have some things still to do in New York this year and I'll think about becoming No 1 after the US Open."
Sabalenka now faces another Grand Slam clash with Keys after beating the American in the quarterfinals at Wimbledon in July.
Keys, who reached the US Open final in 2017, advanced to the last four after defeating Wimbledon champion Marketa Vondrousova of the Czech Republic 6-1, 6-4.
Vondrousova was left ruing her failure to convert any of nine break points that came her way, while Keys was a perfect three-from-three on break points.
"I love playing here, in front of a home crowd – you never feel like you can't get out of any situation," Keys said.
Vondrousova said she had struggled to cope with the power of Keys' serve and groundstrokes.
"I felt like I was under so much pressure from the first point," Vondrousova said. "There wasn't so much to do, honestly. It was very tough. I was just trying to fight, run for every ball. She was just too good."
The match was halted in the first game of the opening set after a spectator required treatment for a medical emergency. US Open organisers later said the incident was not heat-related.
