Peer, ranked 24th, had not made it to a quarterfinal since early March at the BNP Paribas Open. He opponent in Friday's quarterfinal will be eighth-seeded Alberta Brianti of Italy, who needed only 52 minutes to oust American Varvara Lepchenko 6-1, 6-2.
Third-seeded Tamira Paszek of Austria beat American qualifier Madison Brengle 6-3, 6-1 and will play Canada's Stephanie Dubois in the quarters. Dubois advanced by dominating the tempo in the third set against Britain's Heather Watson to win 3-6, 7-5, 6-1.
The other two matchups in Friday's quarterfinals include second-seeded Nadia Petrova of Russia against fifth-seeded Serb Bojana Jovanovski. American Irina Falconi will play Virginie Razzano of France.