Kleybanova defeated Jankovic in the second round 7-5, 6-1. Jankovic had received a bye past the first round, but lost for the third time in four matches on the WTA Tour.
After retiring in the fourth round at Wimbledon, she won just one match in Slovenia before falling in her opening contest at this event.
Kleybanova will next meet either Jie Zheng or Daniela Hantuchova, who will face each other in a second-round match Thursday.
Second-seeded Samantha Stosur moved into the third round with a 6-4, 6-4 decision over Melanie Oudin.
No. 4 Agnieszka Radwanska was a 6-1, 6-3 winner over Dinara Safina and No. 7 Shahar Peer fought past Yaroslava Shvedova 7-5, 6-4.
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