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The German stunned second seed Alcaraz 6-1 6-3 6-7(2) 6-4 in the quarterfinals.
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.
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.
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.
Tournament director Tiley also said Australian Nick Kyrgios could return at the Melbourne Park Grand Slam after he underwent knee surgery in January and suffered wrist and foot issues in an injury-plagued 2023.
The Serbian is the first man to win three Grand Slam events in the same season four times.