The Serb, who is the top seed, eased into the last eight with a comfortable 6-0, 6-2 win over the Russian underdog.
Serena Williams also progressed into the quarters but found it harder going against Katrina Srebotnik. Williams eventually won 4-6, 6-4, 6-3.
After the match Williams said: "I just kept making errors and it wasn't pretty out there. It wasn't the best tennis for me. You know when you're playing and the adrenaline, you really can't assess yourself until the next day. It's kind of frustrating."
Other seeds who made it through were Elena Dementieva, Vera Zvonareva and Agnes Szavay.
There was one minor upset as ninth-seed Zvonareva beat the sixth-seed Marion Bartoli.
In the quarter-finals Serena Williams will face Maria Sharapova, while Jankovic and Zvonareva will clash for a place in the semis.
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