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The 22-time Grand Slam champion overpowered Kubler in 83 minutes to book his place in the last eight.
The American defeated Ukraine's Lesia Tsurenko 6-1, 6-3 in the fourth round.
The 33-year-old Belarusian twice champion has worn shirts showing support for French soccer champions PSG at the tournament and as a gesture to her six-year-old son Leo, who is also a big fan of the Paris club.
Sabalenka surged into the final with a 7-6(1), 6-2 win over unseeded Pole Magda Linette to extend her unbeaten start to the year.
She will join Iga Swiatek, Ons Jabeur, Jessica Pegula, Coco Gauff, Caroline Garcia, Aryna Sabalenka and Daria Kasatkina at the season finale.
The 19-year-old lost to Aliaksandra Sasnovich of Belarus 3-6, 6-1, 6-1.
The All England Lawn Tennis Club, which hosts the grass court Grand Slam, took the decision in the wake of Russia's invasion of Ukraine and the stand was swiftly condemned by the men's and women's tours.
Wildcard Fruhvirtova was leading 6-2, 3-0 when the 32-year-old Azarenka informed the chair umpire that she was done and left the court.
Badosa becomes the first Spanish woman to win the tournament in the California desert.
The Russian rolled back the years as she beat former world No. 1 Victoria Azarenka 5-7, 6-3, 6-2.
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