NEW YORK — There will be a rematch.
They got to this place Tuesday by handling an unpredictable, gusty wind that took tennis balls and made them more like snowflakes, illusory and falling in unexpected places.
The third-seeded Williams, 30 and nine years past her last U.S. Open title, handled the clever pacing from sixth-seeded Francesca Schiavone to win 7-6 (5), 6-4 in 1 hour, 54 minutes.
Then the second-seeded Clijsters, the defending champion, withstood the athletic Samantha Stosur, who was seeded fifth and had played until 1:30 in the morning Monday, winning 4-6, 7-5, 6-3.
Clijsters and Williams are 6-6 against each other in their careers, but Clijsters has won the last four matches, including a 6-0, 0-6, 6-4 upset in the fourth round of the Open last year.
This day of tennis was endlessly entertaining.
Sam Querrey had a chance to advance to his first Grand Slam quarterfinal. But as quickly as Stanislas Wawrinka chipped a service return and snapped off a sneaky volley, a weary Querrey ended up the dejected loser, 7-6 (9), 6-7 (5), 7-5, 4-6, 6-4. The exit of the 20th-seeded Querrey means there are no American men left in the draw.
Williams, who hadn't played since Wimbledon because of a right knee injury, is aiming for her third Open title and her first since 2001.
Williams played in her 33rd major tournament quarterfinal and gave credit to Schiavone. "She played a great match," Williams said. "It's not easy in these conditions. It was hard for both of us to know what decision to make."
Schiavone, 29, who won her first major this year at the French Open, gave Williams some trouble in the first set with her clever changes of pace, but Williams' power took its toll.
In the first 41 years of the U.S. Open at least one U.S. man always had made the quarters, but this is the second year in a row the Americans have all gone home by that point.
Wednesday's featured matches: Wimbledon finalist and seventh seed Vera Zvonareva against 31st-seeded Kaia Kanepi, third-seeded Novak Djokovic against 17th-seeded Gael Monfils, 2009 finalist and top seed Caroline Wozniacki against unseeded Dominika Cibulkova and five-time champion and second seed Roger Federer against fifth-seeded Robin Soderling.