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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.
Third seed Coco Gauff served up 17 double faults but still managed to beat China's Yuan Yue 6-4, 6-3 to reach the women's semifinals in the Californian desert for the first time.
The 22-year-old fourth seed is the first Italian to win the Melbourne Park title.
Sinner broke for a 3-1 lead in the fourth set and ran away with the match to snap the Serb's 33-match winning run at Melbourne Park and end his quest for a record 25th major.
Sinner's victory snapped Djokovic's winning streak of 33 matches at the Australian Open going back to 2018 and was the world No 1's first loss in 11 Melbourne semifinals.
Russian teenager Mirra Andreeva produced a thrilling comeback from 5-1 down in the third set to beat Frenchwoman Diane Parry 1-6, 6-1, 7-6(5).
More than three hours of playing with one of the best players of all time started to take its toll on Prizmic and Djokovic drove home his advantage to take his 90th win at the Australian Open in just over four hours.
Italy's No. 1 Sinner produced a devastating display to outclass a helpless De Minaur after Matteo Arnaldi outlasted Alexei Popyrin in the first singles clash.
A sell-out crowd in Turin's Pala Alpitour had hoped to cheer the 22-year-old Sinner to the biggest title of his career but Djokovic was simply in a different league.
The 20-year-old Alcaraz, who also has won six titles this season, missed out on becoming the youngest finalist in the season-ending tournament since Pete Sampras in 1991.
Results 21-30 of 33
