Shahar served up six aces and saved 9-of-10 break points while beating Japan's Ryoko Fuda 6-4, 6-2.
Petrova needed exactly 1 hour to dispatch U.S. qualifier Alexandra Mueller 6-2, 6-2.
Third-seeded Tamira Paszek of Austria also advanced after winning her battle with American Melanie Oudin 7-6 (7-2), 3-6, 6-2.
The only seeded player beaten Tuesday was Australian Jelena Dokic, seeded fourth, who fell to Zhang Shuai of China 6-3, 6-4.
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