The early part of the second round played mostly to form, with former No. 1-rated players Kim Clijsters and Martina Hingis each moving up in straight sets and upsets relegated to lower-seeded players.
Those who were ousted Thursday were 17th-seeded Anna-Lena Groenefeld, who lost to Ashley Harkleroad 6-2, 6-2, and 24th-seeded Samantha Stosur, who was beaten by Jelena Kostanic Tosic 6-4, 2-6, 6-2.
Sharapova won her first set Thursday at 6-0 and breezed through second at 6-3 in dispatching Anastassia Rodionova. Her next opponent is 30th seeded Tathiana Garbin.
Clijsters, the No. 4 seed, was on the court just 59 minutes in posting a 6-3, 6-0 win over Akiko Morigami, which pairs her against 29th-seeded Ukrainian Alona Bondarenko in the third round.
Hingis was only slightly more tested, winning 6-2, 6-2 over Alla Kudryavtseva and next meets Aiko Nakamura.
Also Thursday, No. 8 Patty Schnyder handled Shuai Peng 7-5, 6-3; No. 9 Dinara Safina stopped Youlia Fedossova 6-3, 6-2; 12-seeded Anna Chakvetadze got past Laura Granville 6-2, 5-7, 6-1; 13th-seeded Ana Ivanovic held off Agnieszka Radwanska 6-2, 3-6, 6-2; 15th-seeded Daniela Hantuchova overcame Emilie Loit 4-6, 6-3, 6-4; and 19th-seeded Chinese Na Li leveled Spaniard Lourdes Dominguez Lino 6-0, 6-2.