The 26-year-old Wozniacki will play Kristina Mladenovic in the final on Sunday after the Frenchwoman beat Australian youngster Daria Gavrilova 7-5 6-3.
Denmark's Wozniacki, who is yet to lose a set in the tournament, struggled to hold serve in the opening stages but held her nerve to break Jankovic's serve five times and come out on top in a battle between two former world number ones.
Wozniacki, who won the Pan Pacific Open last month, will look to secure her second Tour title of the year when she takes on Mladenovic.
Gavrilova defeated world number one Angelique Kerber on Friday, but the Australian was brought back down to earth by the unseeded Mladenovic.
She will be bidding to win her first major singles title on Sunday but will need to record her first victory over Wozniacki who has won both their meetings.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
