Williams needed only 87 minutes to get past the 15th-seeded fellow American Sloane Stephens 6-4, 6-1, firing six aces on her way to the fourth-round victory.
The defending champ has won four U.S. Open titles overall.
The news wasn't as good for Poland's Radwanska, however, who was upended by 24th-seeded Russian Ekaterina Makarova 6-4, 6-4, keeping intact her record of never having reached the New York quarterfinals.
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