Wednesday's 16 first-round matches in the women's draw kicked off one of the year's biggest events outside the major championships. The 32 seeded players in both the men's and women's competitions receive a bye past the first round and play will continue in the California desert until March 17.
Schiavone was ranked as high as No. 4 in the world early in 2011, but is now 47th in those rankings and unseeded in this tournament.
Burdette jumped into the spotlight last year by reaching the third round of the U.S. Open before she turned professional. This, however, was her first match of the year in a WTA Tour event.
She had tried and failed to qualify for two previous tourneys before downing Jana Cepelova and Melinda Czink in qualifying for this championship. Cepelova and Czink were both quarterfinalists last week at a tour stop in Brazil.
In other opening-round matches Wednesday, Olga Govortsova defeated Mandy Minella 6-2, 3-6, 6-4, Shahar Peer was a 6-3, 6-4 winner over Marina Erakovic and Svetlana Kuznetsova breezed past Andrea Hlavackova 6-3, 6-1.
Govortsova will meet fifth-seeded Petra Kvitova in the second round.