That created a third-round matchup against 25th-seeded Carla Suarez Navarro, who was a 6-1, 6-1 winner over Silvia Soler-Espinosa. It will be the first meeting between Sharapova and Suarez Navarro.
Burdette, having recovered from minor wrist surgery late last year, continued to impress in her first WTA event of the season.
Having tried and failed to qualify for two previous tournaments this year, she won two qualifying matches this week just to get in the field and now has advanced to the third round.
After downing veteran Jilly Craybas in the opening round on Wednesday, Burdette defeated No. 23 seed Tamira Paszek 7-6 (7-0), 6-1.
Burdette will take on 13th-seeded Maria Kirilenko in the third round after Kirilenko fought past Christine McHale 4-6, 6-4, 6-1.
In another surprise Svetlana Kuznetsova ousted No. 18 Jelena Jankovic 0-6, 6-2, 7-5. Fifth-seeded Petra Kvitova got past Olga Govortsova 6-4, 3-6, 6-3 and No. 6 Sara Errani survived against Lourdes Dominguez Lino 6-2, 3-6, 6-3.