The 30-year-old Pole, ranked world No. 19 by the Women's Tennis Association (WTA), defeated the 80th-ranked Czech player 7-6, 4-6, 6-4 in their second-round clash in the Spanish capital on Thursday.
Up next for Linette at the clay-court tournament in Madrid is 15-year-old Russian Mirra Andreeva.
Meanwhile, Poland’s world No. 1 Iga Świątek is due to play Austria's Julia Grabher in the second round on Friday.
Świątek missed last year's Madrid Open due to a shoulder injury.
The 2023 Madrid Open runs until May 7.
(gs)
Source: IAR, PAP