Zvonareva dropped the first set but fought back to win 2-6, 6-3, 6-4 at the Khalifa Tennis Complex.
The Russian is now 3-0 in the round-robin event. Jankovic is 2-1.
Elena Dementieva won her match in a walkover when her opponent, American Serena Williams, withdrew with a stomach muscle problem
Zvonareva is playing in the four-woman White Group. She will next play Dementieva and Jankovic goes against American Venus Williams, who is 3-0 in the four-player Maroon Group.
Dementieva, an Olympics gold medalist, is 1-1 in the Maroon Group.
Notable deaths of 2014 [PHOTOS]