Peer had the toughest time of the four top seeded players in the second round, needing to win a seventh game in the first set and then claiming a 7-5, 6-2 win over Tsvetana Pironkova.
Top-seeded Vera Zvonareva advanced on a walk-over when Magdalena Rybarikova was forced to withdraw because of a lower-back injury. Also Thursday, No. 3-seeded Victoria Azarenka was a 6-2, 6-2 winner over Tatiana Poutchek and fourth-seeded Katarina Srebotnik blitzed Melinda Czink 6-0, 6-2.
In the other matches Thursday, Czech players advanced with seventh-seeded Klara Zakopalova stopping Vera Dushevina 6-4, 1-6, 6-3 and Iveta Benesova beating Akgul Amanmuradova, 6--2, 4-6, 6-3.
Friday's quarterfinals have Zvonareva playing Roberta Vinci, Peer meeting Zakopalova; Azarenka going against Karolina Pliskova and Srebotnik facing Benesova.