Williams needed 56 minutes to decimate the Czech Republic's Andrea Hlavackova, 6-0, 6-0, as the Olympic gold medalist eased into the final eight at Arthur Ashe Stadium.
The American star's next opponent will be former world No. 1 Ana Ivanovic, who advanced with a 6-0, 6-4 decision over Bulgarian Tsvetana Pironkova at the USTA Billie Jean King National Tennis Center.
The 12th-seeded Serb, making her first appearance in a major quarterfinal since winning the 2008 French Open, is 0-3 lifetime against Williams.
Poland's Radwanska, meanwhile, was upended by 20th-seeded Italian Roberta Vinci 6-1, 6-4 at Armstrong Stadium.
Vinci bested Radwanska for the first time in five career matches and now goes on to face doubles partner and fellow Italian Sara Errani, who surprised sixth-seeded German Angelique Kerber 7-6 (7-5), 6-3 to reach at least the quarterfinals at three of this year's four Grand Slam events.