Schnyder, seeded second in this event, defeated Nuria Llagostera Vives 6-2, 6-2. Defending champion Sara Errani, the fifth seed, ousted Patricia Mayr 7-6 (8-6), 6-1.
In Friday's quarterfinals, Schnyder will meet Anna-Lena Groenefeld and Errani will face Yaroslava Shvedova. Groenefeld eliminated Arantxa Rus 7-6 (7-5), 6-3 and Shvedova was a 6-3, 6-2 winner over Alberta Brianti.
The other quarterfinals will send top-seeded Flavia Pennetta against Aravane Rezai and Tathiana Garbin against Olga Govortsova.