The 23-year-old, ranked world No. 2 by the Women's Tennis Association (WTA), saw off Czech player Linda Nosková 6-4, 6-2 in the third round on Saturday.
The Polish star, who is the defending champion in Madrid, will now face 13th-seeded Diana Shnaider of Russia for a place in the quarterfinals.
Świątek lifted the trophy in Madrid last year but is still seeking her first title of the season.
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.
(gs)
Source: IAR, PAP