The tournament was hampered by rain through the day Thursday. The start of play was delayed 4 1/2 hours and several scheduled matches, including top-seeded Serena Williams' second rounder, were postponed to Friday.
Jankovic cruised through the first set in 28 minutes but then had to hold off Kaia Kanepi for a 6-2, 3-6, 6-4 victory. Jankovic had two breaks in the first and third sets while dropping serve just twice herself in the match.
No. 5-seeded Elena Dementieva had only a slightly easier time advancing to the third round with a 6-2, 7-6 (7-3) win over Anabel Medina Garrigues that took more than 2 hours.
Eighth-seeded Agnieszka Radwanska was ousted in straight sets, losing 7-5, 6-3 to Yaroslava Shvedova, and 21st-seeded Vera Zvonareva was also upset, losing 6-4, 6-4 to Anastasia Rodionova.
Also Thursday, Na Li, the 11th seed, took out Stephanie Cohen-Aloro 6-2, 6-2; 17th-seeded Francesca Schiavone romped by Sophie Ferguson 6-2, 6-2; 18th-seed Shahar Peer rallied for a 3-6, 6-0, 6-1 win over Bethanie Mattek-Sands; and No. 28-seeded Alisa Kleybanova ran past Ana Ivanovic 6-3, 6-0.
No. 27-seeded Alona Bondarenko was a 6-3, 6-3 winner over Magdalena Rybarikova but her sister Kateryna Bondarenko, the No. 32 seed, was eliminated by Aleksandra Wozniak 6-4, 6-1.
Unseeded Jarmila Groth advanced to the third round by beating Kimiko Date Krumm 6-0, 6-3.
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