Jankovic edged past Caroline Garcia 7-6 (9-7), 4-6, 7-6 (7-2) in a match in which both players won 113 points. Jankovic needed two breaks in the third set to get into the final tiebreaker.
She dropped serve five times on the day while Garcia suffered four breaks.
Third-seeded Peng Shuai and No. 4-seeded Jarmila Gajdosova were also pushed to three sets. Peng dropped serve three times in the second set of a 6-1, 4-6, 6-2 victory over Yvonne Meusburger while Gajdosova played for about 2 1/2 hours in a 1-6, 7-6 (7-2), 7-5 win over Kathrin Woerle.
No. 6-seeded Ayumi Morita defeated Nudnida Luangnam 6-4, 6-0 while losing just four points on serve in the second set, but Hsieh Su-Wei eliminated eighth-seeded Anne Keothavong 6-4, 7-5.
Also Tuesday Karolina Pliskova topped Chang Kai-Chen 6-3, 6-2; Casey Dellacqua beat Bojana Jovanovski 6-0, 6-2; Eleni Daniilidou got past Sania Mirza 6-2, 1-6, 6-4; Jill Craybas advanced with a 6-4, 1-6, 6-4 decision over Yurika Sema; and Krystyna Pliskova, Karolina's twin sister, defeated Iryna Bremond 6-0, 6-2.