Russian Sharapova defeated Czech qualifier Barbora Zahlavova Strycova, 6-1, 6-3. The Australian Open champion and former world No. 1 Sharapova is 19-1 this season, including winning two tournaments. She missed the Sony Ericsson Open in Miami because of a shoulder injury.
Davenport beat fellow American Vania King 6-2, 6-3. The three-time Grand Slam event titlist and former world No. 1 star won this event in 1997, 2004 and 2005.
In a second-round upset, Olga Govortsova of Belarus defeated fourth-seeded Frenchwoman Marion Bartoli, 4-6, 6-2, 6-4.
Also in second-round play Tuesday, eighth-seeded Hungarian Agnes Szavay beat Russian Ekaterina Makarova 6-4, 6-1; 12th-seeded Slovenian Katerina Srebotnik beat Taipei's Yung-Jan Chen 6-4, 6-0; and 13th-seeded Frenchwoman Virginie Razzano beat Poland's Marta Domachowska 6-3, 2-6, 7-6 (7-4.