Rainy conditions on the clay courts of the Foro Italico made for dicey conditions as only nine of the 11 scheduled matches were completed.
Azarenka, the No. 9 seed, breezed to a 6-1, 6-4 straight set win over Kazakh qualifier Sesil Karatantcheva.
Meanwhile, 14th-seeded Petrova had little trouble with Italy's Tathiana Garbin, 6-3, 6-2.
In a minor upset, 15th-seeded Russian Vera Zvonareva fell victim to Petra Kvitova of the Czech Republic, 6-4, 6-0.
Other winners Sunday included Russia's Maria Kirilenko and Italians Alberta Brianti and Maria Elena Camerin.
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