Russian Maria Sharapova, top seed, reached the third round at the 600,000-dollar Los Angles Classic tournament Wednesday as her opponent Eleni Daniilidou retired in the second set.
Sharapova, who won her first title of the season in San Diego on Sunday, had to battle to take the first set 7-6 (7-5) but was up 3-1 in the second when Greece's Daniilidou decided she couldn't continue.
She said she was still feeling the effects of an illness that had prevented her from practicing.
Jankovic, runner-up to Russian Elena Dementieva here last year, managed to shrug off the after-effects of a cold to defeat China's Peng Shuai 6-1, 6-1.
Her compatriot Ana Ivanovic, the third seed, also advanced, defeating American Ashley Harkleroad 6-4, 6-2.
In the third round Sharapova will face Michaella Krajicek of the Netherlands, who advanced on Tuesday.
Ivanovic was playing for the first time since falling in the semi-finals at Wimbledon to eventual champion Venus Williams and booked a clash with Czech Lucie Safarova, who beat Ai Sugiyama.
In other matches, Israeli Shahar Peer's struggles continued as she fell 6-1, 4-6, 7-6 (8-6) to France's Virginie Razzano.
Up next for Razzano is India's Sania Mirza, who is having one of the best summers of any player on the tour. The 20-year-old upset No. 7 Martina Hingis in the second round on Tuesday.
Defending champion Dementieva needed just 54 minutes to dismiss American wild card Madison Brengle 6-2, 6-0.
She next faces fifth-seeded Daniela Hantuchova of Slovakia, 6-3, 7-6 (7-5) winner over American Jill Craybas.
Fourth-seeded Russian Nadia Petrova also advanced, beating American Lilia Osterloh 7-5, 6-3.