Jankovic captured the first set against Davenport Friday before Davenport was forced to retire.
Davenport has won this tournament twice and has been a runner-up four times.
Friday's other semifinal will send second-seeded Svetlana Kuznetsova against No. 4 seed Maria Sharapova.
Kuznetsova lost in the finals of this tournament last year to Daniela Hantuchova. Sharapova has an 18-0 match record this year, a streak that includes a title at the Australian Open.
Dennis Rodman pledges to end trips to North Korea
Scarlett Johansson steps out with fiance after pregnancy reveal