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.
WC Debate: Who Are The Greatest-Ever World Cup Nation?
Peer reaches Korea Open quarters
Kirilenko advances at Korea Open
Canobbio: I Need Confidence
