Peer ousted third-seeded Chanelle Scheepers 2-6, 7-5, 6-3 in about 2 1/2 hours. Both players had six breaks but three of those against Peer came in the first set. She had just one -- winning five of the six break third-set chances Scheepers had -- in the final set.
She heads into Friday's quarterfinals against Tadeja Majeric, who recorded a tight 7-6 (7-5), 6-3 decision over Tereza Martincova. Majeric won just four more points (87-83) overall but clinched the match with three second-set breaks.
Seventh-seeded Elina Svitolina stopped Nastassja Burnett 6-0, 7-6 (7-3), losing her serve once on the day.
Also Thursday, qualifier Magda Linette advanced with a 3-6, 6-1, 6-2 decision over Kristyna Pliskova and Galina Voskoboeva outlasted Kateryna Kozlova 4-6, 6-3, 6-1.
Voskoboeva draws fourth-seeded Alexandra Cadantu and Svitolina meets No. 2-seed Donna Vekic in quarterfinals from the lower half of the draw. In addition to the Peer-Majeric quarterfinal, Linette goes against Ons Jabeur on Friday.