Medvedev defeated Alcaraz 7-6 (7/3), 6-1, 3-6, 6-3 to reach his fifth major final and stop Alcaraz in his quest to become the first man to retain the title in New York since Roger Federer in 2008.
"I said I needed to play 11 out of 10. I played 12 out of 10, except from the third set," said the 27-year-old Medvedev.
"He (Alcaraz) is honestly just really unbelievable. To beat him you need to be better than yourself and I managed to do it.”
Rematch of 2021 final
Medvedev now meets Djokovic on Sunday as the 36-year-old Serbian star once more goes in search of a record-equalling 24th Grand Slam title to crown his return to world number one next week.
The third-seeded Medvedev won his lone major at the 2021 US Open when he foiled Djokovic in his bid for a calendar Grand Slam, leaving his rival in tears after a straight-sets triumph.
He produced another scintillating performance against Alcaraz, avenging a lopsided loss to the Spaniard in the Wimbledon semi-finals in July.
Medvedev held his nerve under constant pressure from Alcaraz in the opening set, elevating his level in tie-break to claim the final four points.
"I totally lose my mind on that set, and fighting for 50 minutes and then, you know, for four points lose my mind. It was really tough for me to handle it," said Alcaraz.
Alcaraz didn't face a single break point in the first set, but Medvedev totally dominated the second set -- dropping just two points on serve and breaking the top seed twice.
The 20-year-old Alcaraz kept his hopes alive with a break in the fourth game of the third set enough to extend the match to a fourth set.
He saw three break points come and go at 1-1 before Medvedev administered the fatal blow with a superb backhand return, breaking for a 4-2 lead.
A routine hold moved Medvedev to the cusp of victory, which he eventually sealed after an epic final game in which Alcaraz saved three match points but also failed to convert three break points.
"I thought that right now I am better player to find solutions when the match is not going in the right direction for you," said Alcaraz.
"But, you know, after this match, I gonna change my mind. I'm not mature enough to handle these kind of matches. So I have to learn about it."
Djokovic outwits Shelton
Djokovic ended the run of unseeded 20-year-old American Ben Shelton earlier on Friday, winning 6-3, 6-2, 7-6 (7/4) to advance to his 10th US Open final in 17 appearances.
"Another Grand Slam final. I cannot be happier with where I am," said Djokovic, who missed last year's tournament at Flushing Meadows because of his refusal to be vaccinated against Covid-19.
Djokovic is attempting to become the oldest men's champion in New York in the Open era, which would also see him match Margaret Court's all-time mark for most major singles titles.
The Serbian has now won 22 of his last 23 Grand Slam semi-finals. He captured the last of his three US Open titles in 2018.
Djokovic has reached the final at all four majors in the same year for the third time. He will try to claim three Grand Slams in the same season for the fourth time in his career.
"I'm obviously over the moon with the results so far on Grand Slams," said Djokovic.
"Playing in all four finals of all four Slams in a season is amazing. It's the highest achievement I can think about when I start the season.
"That's what I dream about, that's what I really wanted, that's where I want to be, in this kind of position.”
‘Every loss hurts’
Djokovic's only Grand Slam loss this year came at Wimbledon when he was beaten by Alcaraz in five sets.
Shelton began the US Open ranked 47th but will break into the top 20 for the first time on Monday.
"There's a small piece of it is disappointment obviously. I'm a competitor," he said. Every loss hurts. It cuts you a little bit.
"But if anything, this week has just motivated me more."