Clijsters, a Melbourne finalist in 2004, underlined her billing as tournament favourite but was forced to scrap by 12th seed Radwanska in unseasonably chilly conditions.
The Belgian, who won the third of her three U.S. Open titles last year, traded breaks at the start with her Polish opponent before taking the first set in 29 minutes.
Radwanska forced a tiebreak in the second, but Clijsters quickly snuffed out the danger, sealing it 7-4 with a bullet of a backhand to set up a clash with second seed Vera Zvonareva.
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