Petrova had been enjoying the form of her life during the claycourt season earlier this year -- winning three consecutive tournaments -- but a groin injury picked up in the run-up to the French Open appears to have completely thrown her off course.
The left leg strain put paid to her Roland Garros campaign, where she lost in the opening round, and after opting out of the tour for two months to recuperate, she has failed to win a match in three attempts since making her comeback.
Chakvetadze, who also beat Petrova in San Diego earlier in the month, will next play Nathalie Dechy of France, who knocked out 15th-seeded Russian Maria Kirilenko 6-4 6-4.
Fellow Russian Anastasia Myskina continued her unpredictable run of form by exiting at the hands of Israel's Shahar Peer.
The sixth seed went down 7-6 5-7 6-4 for her second defeat at the first hurdle in three tournaments after reaching the final in Stockholm last week.
Fourth seed Svetlana Kuznetsova had little difficulty moving on, defeating Polish qualifier Marta Domachowska 6-1 6-3.
Other seeded players also fell to the wayside on Wednesday, with American qualifier Shenay Perry outslugging 10th seed Anna-Lena Groenefeld of Germany 7-6 6-2.
Serbia's Jelena Jankovic defeated number eight Francesca Schiavone of Italy, 6-1 6-4, and Japan's Ai Sugiyama upset 17th seed Anabel Medina Garrigues of Spain 6-4 6-2.
Italy's Flavia Pennetta, the 12th seed, had to retire in the second set trailing 7-5 2-1 against France's Marion Bartoli.
Russia's Dinara Safina and Daniela Hantuchova of Slovakia were among the seeded winners.
Top seed Kim Clijsters, the U.S. Open champion, begins her title defence against local wildcard Stephanie Dubois in the featured evening match.
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