Sharapova had a tougher-than-expected battle on her hands before getting past Anabel Medina Garrigues 7-6 (7-3), 5-7, 7-6 (7-1). The match took almost 3 1/2 hours and Sharapova had to rally from a service break down in the third set.
Sharapova, who has a 20-1 match record and three titles this season, will meet Alona Bondarenko in the quarterfinals. Bondarenko defeated Dinara Safina 7-6 (7-5), 0-6, 7-5.
Mauresmo earned her quarterfinal berth by rallying past Agnieszka Radwanska 3-6, 7-5, 7-6 (8-6). Davenport also was taken the distance before defeating Karolina Sprem 6-4, 3-6, 6-4.
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