Martic, the No. 5 seed, took down Jankovic 6-7 (5-7), 7-5, 7-6 (7-5) in just over three hours.
The match was originally scheduled to take place on Saturday, but rain postponed it until Sunday.
The 21-year-old Martic fired nine aces to secure a spot in her first-ever WTA singles final against Taiwanese qualifier Su-Wei Hsieh.
Martic and Hsieh will meet in the final later Sunday.
This week's champion will earn $37,000.