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Alcaraz became the first man to defend a championship in the California desert since Novak Djokovic won three straight between 2014 and 2016.
Alcaraz came from behind to beat Jannik Sinner before Medvedev edged out American Tommy Paul 1-6, 7-6(3), 6-2 in the second semifinal.
The 22-year-old fourth seed is the first Italian to win the Melbourne Park title.
Alcaraz will face Green Group runner-up Novak Djokovic in a mouth-watering semifinal.
The 20-year-old Alcaraz will need to beat Medvedev in his final group game on Friday.
Rublev, ranked fifth in the world, began to despair after losing the first set and failed to put up much of a fight in the second.
A final involving former US Open champions Medvedev and three-time winner Novak Djokovic on Sunday is one of obvious high quality but not the next chapter in tennis's hottest rivalry of Djokovic and Alcaraz that has had the sport buzzing.
On another steamy hot day with temperatures in the mid-90s Fahrenheit (32 Celsius) Medvedev was better able deal with the stifling humidity and heat inside Arthur Ashe Stadium than eighth seed Rublev to make the Flushing Meadows semi-finals for the fourth time in five years.
Sabalenka faces China's Zheng, who knocked out 2022 finalist Ons Jabeur, in the qusarterfinals.
The British charge at the US Open will carry on without 2012 champion Andy Murray, who was outclassed by Bulgarian Grigor Dimitrov.