Clijsters, seeded second behind Caroline Wozniacki, breezed past Petra Kvitova in an afternoon match 6-3, 6-0. Williams, playing in the evening, was a 6-2, 6-1 winner over Mandy Minella.
In the round of 16, Clijsters will meet Ana Ivanovic, who got past Virginie Razzano 7-5, 6-0. Williams will meet Shahar Peer, who disposed of Flavia Pennetta 6-4, 6-4.
Clijsters has won 17 consecutive matches at the U.S. Open and is trying to become the first woman to successfully defend her title in this event since Williams did so in 2001. If they each win two more matches, Clijsters and Williams will meet in the semifinals.
Also advancing was French Open champion Francesca Schiavone, the sixth seed. She defeated Alona Bondarenko 6-1, 7-5 and will now face rising star Anastasia Pavlyuchenkova.
Pavlyuchenkova easily downed Gisela Dulko 6-1, 6-2. Schiavone is trying to climb out of a slump that has affected her since she claimed her first major championship. After winning in Paris, she lost in either the first or second round in five out of six tournaments.
Another round of 16 match was set up between Samantha Stosur and Elena Dementieva. Stosur defeated Sara Errani 6-2, 6-3 and Dementieva opened the day's action in Arthur Ashe Stadium by defeating Daniela Hantuchova 7-5, 6-2.
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