The top-ranked Russian, who was runner-up at the French and Australian Opens, beat her Italian opponent 2-6, 7-5, 6-4 in second-round play at the $2 million event.
Safina racked up 10 double faults in the match, which lasted nearly two hours.
Venus Williams of the United States also advanced Tuesday by dispatching Belarusian Olga Govortsova 6-2, 6-2.
French Open champion Svetlana Kuznetsova struggled against Czech Lucie Safarova but eventually prevailed 6-3, 6-7 (2-7), 7-6 (7-4).
Other winners Tuesday included Peng Shuai of China, who downed 15th-seed Dominika Cibulkova of Slovakia, and Ukraine's Alona Bondarenko, who beat No. 10 seed Nadia Petrova 6-2, 6-2.
Flavia Pennetta, who won last week's tournament in Los Angeles, ousted Japanese qualifier Ayumi Morita 6-2, 6-3.
Copyright 2009 by United Press International.
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