After just two rounds, Peer is the only seeded player left in the bottom half of the draw after her 6-4, 7-5 win.
Her quarterfinal opponent will be American veteran Jill Craybas, who downed towering Uzbek Agkul Amanmuradova 7-6 (1), 6-2.
The other quarterfinal match to be determined Wednesday will see Australia's Samantha Stosur take on Russian Ekaterina Makarova.
Stosur, regarded more as a doubles specialist, struggled past German Sabine Lisicki 6-4, 6-7 (4), 6-3. Makarova downed Czech Klara Zakopalova 6-3, 6-2.
Top seed Maria Kirilenko will be in action Thursday for her second-round match against Czech Lucie Safarova.
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