Serena Williams crushed fellow American Vania King 6-1, 6-0 in 56 minutes.
Top seed Marion Bartoli survived a struggle lasting for more than three hours, with the Frenchwoman overcoming a massive 18 double-faults to advanced at the WTA hardcourt event here on Wednesday.
Virginie Razzano and Pauline Parmentier won in contrasting ways to give France a 2-0 lead over Slovenia in their Fed Cup World Group II playoff on Saturday.
Maria Sharapova, who last year reached her first Grand Slam final since 2008, has parlayed 2011's run of success into a solid start to the new WTA Tour campaign.
Japanese veteran Kimiko Date-Krumm and Vania King of the United States won their opening matches at the WTA Tour's Indian Wells tournament on Wednesday.
Former French Open champion Ana Ivanovic has advanced to the fourth round of the Australian Open, beating American Vania King 6-3, 6-4 on Saturday at Margaret Court Arena.
Second-seeded Marion Bartoli was eliminated in the second round of the Korea Open on Wednesday, losing to Vania King of the United States 6-3, 7-5.
Indian qualifier Sania Mirza edged past Vania King in a three-set battle to book a pre-quarterfinal berth in the WTA Family Circle Cup.