Jankovic, seeded second, had to work to get past Sofia Arvidsson 6-3, 6-7 (5-7), 7-5. The match lasted two hours, 45 minutes. Jankovic served for the match at 5-4 in the second, but wound up with nine double faults and had her serve broken eight times.
In the third round, Jankovic will meet Jie Zheng.
Kuznetsova, who has reached the title match in a major championship threw times and who is seeded third in this event, defeated Sorana Cirstea 7-6 (7-3), 6-1. Davenport was a 7-5, 6-3 winner over Alisa Kleybanova.
Elena Dementieva coasted into the third round with her eighth straight match victory, a 6-2, 6-1 defeat of Pauline Parmentier. Dementieva is coming off a win in the Olympic gold medal finals.
The day's biggest upset came when Tatiana Perebiynis defeated eighth-seeded Vera Zvonareva 6-3, 6-3. Zvonareva was the bronze medalist in Beijing.
Celebrity Families of 2014 [PHOTOS]