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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.
Top-ranked Iga Swiatek faces a tricky test against 2020 champion Sofia Kenin first up in the women's section.
The 22-time Grand Slam champion overpowered Kubler in 83 minutes to book his place in the last eight.
The total prize money is A$86.5 million ($58.91 million), an increase of 13.5 per cent from 2023.
The fire broke out at the Coco Latex factory at Moonilavu near Erattupetta.
The win by the cool and collected Swiatek sets up a final showdown with American Jessica Pegula, and she can end the year on top if she is able to hoist the trophy
The second semifinal between Swiatek and top seed Sabalenka was cancelled for the night due to rain.