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Ivanovic claimed one of the best victories of her career when she overcame the Russian 6-2 6-4.
The 17-year-old has leaped up the rankings and beat U.S. Open champion Svetlana Kuznetsova in Miami last month.
World number 10 Zvonareva failed to find any consistency against her opponent, who played aggressive game and always looked the more confident of the two.
"I just tried to play my game, to attack her and get a little bit into court and get her on the move, and I think I did that pretty well," said Ivanovic, who added she was surprised at her rapid progress.
"It's taken a lot of work. I've practised very hard the last few months, and I'm pretty happy to see the results so fast. Now I'm going to practise even harder to continue to improve my game."