Last year's runner-up Ivanovic beat Patty Schnyder - seeded tenth - 6-3, 6-2, while Jankovic knocked out Spaniard Carla Suarez Navarro, winning by the same scoreline.
The winner of the contest will have the chance to become the top ranked woman in the world following Maria Sharapova's exit from Roland Garos at the hands of Dinara Safina and Justin Henin's recent retirement.
Jankovic said of her healthy rivalry with Ivanovic: "I think we are going to be dominating this tennis world soon.
"One of us will reach No. 1 soon, and then it will be depending on who is on form for the rest of the year. We push each other, and we motivate each other to be better players, for sure."
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