Williams, who comfortably beat Iveta Benesova in her first-round match, was made to work hard in the first set by Serb Jankovic before easing to victory in the second.
She now takes on Australian Anastasia Rodionova for a place in the quarter-finals.
Earlier, third seed Marion Bartoli survived a tough battle to make it into the third round.
The world number seven was pushed all the way by Russia's Vera Dushevina before coming through 6-2 6-7(3) 6-4 in a match that lasted more than three hours.
Bartoli now meets 14th seed Polona Hercog, who beat Varvara Lepchenko 6-3 6-2.
Thirteenth seed Nadia Petrova came through a tough three-setter against American veteran Jill Craybas, with the 37-year-old boosting the crowd's hopes of seeing a shock result as she won the opening set.
Petrova took the second set in a marathon tie-break, however, and Craybas faded quickly thereafter to lose 2-6 7-6(8) 6-2. The Russian now plays compatriot Anastasia Pavlyuchenkova.
Number 12 seed Yanina Wickmayer of Belgium was upset 6-2 7-6(2) by Kazakhstan's Yaroslava Shvedova, who will now play Sabine Lisicki after the German sixth seed battled past Andrea Hlavackova 2-6 6-3 6-4.
In other notable results, 17th seed Marina Erakovic came past Anna Tatishvili 7-5 6-3, Aleksandra Wozniak beat Barbora Zahlavova 7-6(5) 6-2 and Galina Voskoboeva beat Paula Ormaechea 6-2 6-3.