Fourth seed Victoria Azarenka secured a last 16 berth with a 7-6 6-3 victory over Slovakian Polona Hercog.
Zheng enjoyed strong support from a partisan crowd in the 15,000-seater arena but the world No.72's hopes of claiming a major scalp were crushed by Radwanska in a 6-1 6-4 defeat.
With French Open champion Li Na a surprise first-round casualty China's sole survivor in the tournament is lowly-ranked wildcard Zhang Ze who faces a daunting task against Frenchman Jo-Wilfried Tsonga in the men's second round on Thursday.
In the men's draw, Spain's Fernando Verdasco came back from a set behind against Italy's Flavio Cipolla, winning 2-6 6-1 6-2 to reach the quarter-finals. Russia's Mikhail Youzhny beat Spain's Feliciano Lopez 6-7 6-2 7-5.
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