Medina Garrigues, the No. 3 seed, eliminated Italian Mara Santangelo, 7-5, 6-0.
Fourth-seeded Aleksandra Wozniak of Canada beat Slovakian Magdalena Rybarikova, 6-3, 6-7 (4-7), 7-5.
Other winners included American Jill Craybas.
The event's top seed, Russia's Elena Dementieva, will meet Taipei's Yung-Jan Chan in her opening match.
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