Safarova used her strong baseline play to constantly trouble Radwanska on her serve, creating 13 break points and converting four of them.
Marion Bartoli of France, the 2007 Wimbledon finalist, beat Alisa Kleybanova of Russia 7-5, 6-2, while Nadia Petrova of Russia ousted Roberta Vinci of Italy 6-4, 6-2.
Bartoli double-faulted five times in the first set and was broken once before gradually taking control against Kleybanova. In the second set, she lost just five points on her serve.
"It was a windy day and that's why I took time to settle down," Bartoli said. "I had a bad start but managed to find my rhythm in the second set."
Top-ranked Caroline Wozniacki of Denmark has a first-round bye, as do the next three seeded players: Vera Zvonareva of Russia, Francesca Schiavone of Italy and Li Na of China.
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