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The Spaniard won 6-7(1) 6-3 6-4 6-4 against the lanky Russian.
Jasmine Paolini blazed past American Emma Navarro 6-2 6-1 to become the first Italian woman to make the Wimbledon semifinals.
Second seed Coco Gauff was also not at her best but reined in the errors to get past Romanian qualifier Anca Todoni 6-2 6-1.
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.