Eleventh seed Ivanovic went down 6-4 6-3 to Swiss Romina Oprandi, ranked 69th in the world.
Ivanovic struggled with her service placement, getting in just 46 per cent of her first serves, and was broken five times.
Oprandi will play either world number one Victoria Azarenka or Elena Vesnina in the last eight.
Ivanovic's fellow Serb Jankovic was also defeated in straight sets, 7-5 6-4 by Carla Suarez Navarro of Spain.
In a match where to serve seemed a hindrance, Jankovic converted seven of 23 break points while Suarez Navarro converted nine of 18 break chances.
The world number 46 faces ninth seed Marion Bartoli of France in the quarter-finals after she beat Julia Goerges 6-3 7-6(2).
The German struggled to keep up with Bartoli's rallying in the first set and sacrificed accuracy for power with her first serve in the second set in an attempt to dominate those points, with improved results. However she was swamped in the tiebreak and bowed out of the tournament.
Third seed Agnieszka Radwanska was outplayed in the first set but roared back to beat qualifier Lourdes Dominguez Lino 2-6 6-1 6-4 and reach the last eight.
The Pole failed to convert either of her break points in the first set with Dominguez Lino, who was up on Radwanska in all areas stats-wise, making the most of both of hers.
The Spaniard suffered a meltdown in form in the second set, winning just two points on her serve. She improved in the decider, a set that featured seven breaks of serve, but the momentum was with Radwanska.
Second seed Maria Sharapova eased through to the third round of the tournament with a 6-2 6-2 win over Sorana Cirstea in an hour and 18 minutes. The Russian faced only one break point as she dominated throughout.
Also in the second round, Polona Hercog of Slovenia beat Ekaterina Makarova of Russia 7-6(5) 3-6 7-6(3).
- Carla Suarez Navarro
- Agnieszka Radwanska
- Romina Oprandi