Both players threatened to break in the early stages, but it was Ivanovic who eventually went 2-1 ahead thanks to a big forehand return. She then consolidated her break to edge further clear.
A double break put Ivanovic in complete command of the first set at 5-2, but Jankovic struck back to keep the set alive.
Ivanovic was having trouble putting the set to bed, and looked to have blown her opportunity when Jankovic won her fourth straight game to level it at 5-5.
Just as Jankovic had built up a head of steam at 40 on her own serve, she crumbled. Ivanovic doggedly fought back to break, before this time closing out the set 7-5.
Once again, Ivanovic broke in the third game to establish an early lead in the second set.
There were no mistakes this time as the two players matched each other blow for blow, with Ivanovic breaking once more in prevailing 7-5 6-3.
She now faces Agnieszka Radwanska in the fourth round.