Ivanovic, whose French Open victory was one of two tournament triumphs this year, got past Petra Kvitova 6-3, 4-6, 6-3 to set up a third-round match against Tamira Paszek.
Paszek was a 6-4, 7-5 winner over qualifier Melinda Czink.
Jelena Jankovic, seeded second, had an easy 6-0, 6-4 victory over Aleksandra Wozniak in an evening match. Jankovic will next meet Stephanie Dubois, who was a surprise winner over 13th seeded Maria Kirilenko 6-2, 2-6, 7-6 (7-4).
Third-seeded Maria Sharapova also advanced with a 7-5, 5-7, 6-2 victory over Marta Domachowska. Next up for Sharapova will be Ai Sugiyama, who breezed past Shahar Peer 6-2, 6-2.
Among the seeded winners Wednesday were Nadia Petrova, Patty Schnyder and Dinara Safina, who won last week's East-West Bank Classic in Carson, Calif.
Celebrity Families of 2014 [PHOTOS]