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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.
Gauff set up a semifinal clash with Sabalenka in a rematch of last year's US Open final.
The top remaining seed after Saturday's early exit for world No. 1 Iga Swiatek, Sabalenka's biggest enemy has often been her own emotions but she continued to keep them strictly under control to reach the last eight without dropping a set.
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).
Fourth seeds Coco Gauff and Jannik Sinner, along with home hope Alex de Minaur and world number 11 Barbora Krejcikova progressed.
Yastremska, the world No. 93 who reached the third round at Melbourne Park in 2019, secured the early break in the second set as her opponent continued to spray the errors and the 23-year-old held firm to seal the victory.
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.
Top-ranked Iga Swiatek faces a tricky test against 2020 champion Sofia Kenin first up in the women's section.