The Polish world No. 2 dispatched the 13th-ranked Russian player 6-0, 6-7, 6-4 in the women's singles round of 16 on Tuesday.
The 23-year-old Pole, who is the defending champion in Madrid, will now face the winner between American Madison Keys and Croatian Donna Vekić for a place in the semifinals.
Świątek lifted the trophy in Madrid last year, but this season she has struggled with inconsistency and has yet to claim a title.
Earlier this month, she made a quarterfinal exit in Stuttgart.
Świątek in October parted ways with her longtime Polish coach Tomasz Wiktorowski and hired Belgium's Wim Fissette to replace him.
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Source: IAR, PAP