Fourth-seeded Jankovic of Serbia defeated Slovakian Daniela Hantuchova 7-5, 6-2. Jankovic next plays Russian Elena Vesnina.
Russian Alisa Kleybanova, 19, defeated Williams in 6-3, 3-6, 7-5. Williams beat Kleybanova in the fourth round at Wimbledon last season.
In other second-round action involving seeded players, Dane Caroline Wozniacki beat American Varvara Lepchenko 6-3, 6-1 and former top-ranked Frenchwoman Amelie Mauresmo beat Zheng Jie of China 6-2, 7-5.
Mauresmo, two-time major champion Mauresmo, plays Olympic gold medalist Elena Dementieva Wednesday.
Notable deaths of 2014 [PHOTOS]