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Elena Rybakina also booked a third round spot with a 6-3, 6-3 victory over rising Czech teenager Linda Noskova.
By winning her 30th career title, the former world No. 2 Kvitova will now re-enter the top 10 for the first time since September, 2021.
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.
Azarenka rolled back the years as the two-time champion crushed third seed Jessica Pegula 6-4, 6-1.
Jelena Ostapenko stunned Coco Gauff 7-5, 6-3 to reach the quarterfinals after putting on a power-hitting clinic.
The 23-year-old asking the federation to instead invest the money in promoting tennis at the grassroots-level in the country.
The big-serving 23-year-old, who was born in Moscow and reportedly still lives there, switched allegiance to Kazakhstan four years ago to gain more financial support.
Results 11-17