Schnyder, who won the tournament two years ago, has captured 17 of her last 21 matches. She will meet Akiko Morigami in the quarterfinals Friday.
Elsewhere in the second round Thursday, No. 6 seed Elena Vesnina got past Meng Yuan, 6-1, 6-4; Olga Govortsova ousted ninth-seed Jill Craybas, 6-7 (5-7), 6-3, 6-1; and Akgul Amanmuradova came back to defeat Bethanie Mattek, 2-6, 7-5, 7-6 (7-4).
Vesnina will meet top-seeded Anna Chakvetadze in the quarterfinals.