The sixth-seeded Jankovic, from Serbia, had seven double faults and was successful on only 59 percent of her first serves.
Radwanska advanced to the quarterfinals against top-seeded Victoria Azarenka of Belarus. It is just the fourth time this season Radwanska has reached the quarters.
Radwanska, ranked No. 39, has five top-20 wins this season after defeating Jankovic, ranked 16th.
Seventh-seeded Ana Ivanovic of Serbia was pushed early before she settled down to beat qualifier Coco Vandeweghe 7-6 (5), 6-3 win in a night match.
Vandeweghe, from nearby Rancho Santa Fe, wo five consecutive points to take a 5-2 lead in the first set tiebreaker. Ivanovic then reeled off the final five points, including a crosscourt forehand winner to win the set.
Ivanovic jumped out to a 4-0 lead in the second set before needing four match points to advance to the quarterfinals against fourth-seeded Roberta Vinci.
Wild-card entrant Virginie Razzano of France also advanced with a 6-1, 6-4 victory over eighth-seeded Carla Suarez Navarro of Spain. Razzano, who beat two-time Grand Slam singles champ Svetlana Kuznetsova of Russia in the first round, will face third-seeded Petra Kvitova of the Czech Republic.
Radwanska's sister, Agnieszka, moved into the quarterfinals with a 6-3, 6-3 victory over Daniela Hantuchova of Slovakia. Agnieszka Radwanska, the No. 2 seed, will face fifth-seeded Sam Stosur.
Hantuchova, who is teaming with former top-ranked singles player Martina Hingis in doubles, has lost to Agnieszka Radwanska in the tournament three of the last four years.