Jankovic, the world's fourth-rated woman's player, had little trouble with Sanda Mamic in a 6-2, 6-2 victory. Williams, rated seventh, faltered slightly in a 6-2, 6-7 (6-8), 6-2 match with Shuai Peng.
Both moved into Friday's quarterfinals where Jankovic will go against Zi Yan, who was a 6-2, 6-2 winner Thursday over Olga Savchuk, and Williams plays seventh-seeded Vera Zvonareva, who was a 7-6 (7-5), 6-1 victor over Agnes Szatmari in her second-round match.
If both Williams sisters win on Friday, they would square off in the Saturday's semifinals.
The 2008 Bangalore Open winner will take home $95,500.