The 15th-seeded Stephens hung with the defending champ for most of the first set. After Williams broke to go up 4-2, she broke right back.
Serving at 4-5, Stephens had six of her 29 unforced errors. She was able to save two set points, but twice failed to capitalize when she had a chance to close out the game.
When Stephens hit a forehand wide, Williams had the set, and she took over from there.
"Obviously, she's No. 1 in the world for a reason,'' Stephens said. "I thought she played really well herself. Obviously, it didn't go how I wanted. The second set got away from me a little bit. All in all, I thought I competed well and played well. That's all you can do, really.''
Williams will face 18th-seeded Carla Suarez Navarro, who needed 2 hours, 41 minutes to edge eighth-seeded Angelique Kerber 4-6, 6-3, 7-6 (3).
Earlier on a humid day at Arthur Ashe Stadium, defending men's champion Andy Murray staggered around the court between points.
Once a point started, he sprinted down every ball, as usual. Struggling with his breathing, Murray needed a set to find his rhythm against 47th-ranked Florian Mayer, then rolled the rest of the way to a 7-6 (2), 6-2, 6-2 victory in the third round.
It's classic Murray to grimace in apparent pain after losing a point, then race across the court to hit a winner with no hint of discomfort. Even if his expressions didn't show it, the third-seeded Scot is enjoying the role of reigning champ at Flushing Meadows.
It was here a year ago that he cured 76 years of tennis misery for Britain, its first men's Grand Slam winner since 1936. Then back home for Wimbledon in July he ended its drought there, too, with the first title in 77 years.
"The expectations are higher, but there's not as much pressure to win,'' Murray said in an on-court interview. "I feel much more comfortable coming into these events than this time last year.''
He'll next face 65th-ranked Denis Istomin of Uzbekistan, who won a five-setter against No. 20-seeded Andreas Seppi 6-3, 6-4, 2-6, 3-6, 6-1.
Fifth-seeded Tomas Berdych played his match on the Grandstand, the third-largest stadium at the U.S. Open. In a sport dominated by four players, Berdych is easily overlooked. But he is cruising so far at Flushing Meadows, where he reached the semifinals last year after beating Roger Federer.
The Czech routed No. 31-seeded Julien Benneteau 6-0, 6-3, 6-2 and has yet to drop a set at this year's U.S. Open.
Berdych, who lost to Rafael Nadal in the 2010 Wimbledon final, will face ninth-seeded Stanislas Wawrinka in the round of 16.
Wawrinka beat Marcos Baghdatis 6-3, 6-2, 6-7 (1), 7-6 (7).
Lleyton Hewitt, the 2001 U.S. Open champ, returned to the round of 16 at Flushing Meadows for the first time since 2006. At age 32, the Australian is back from years of injuries to make another run. He beat 102nd-ranked Evgeny Donskoy 6-3, 7-6 (5), 3-6, 6-1.
Top-seeded Novak Djokovic is scheduled to open the night session against Joao Sousa.
Bob and Mike Bryan were down a set and a break against unseeded Canadians Daniel Nestor and Vasek Pospisil in their third-round doubles match before rallying for a 6-7 (1), 7-5, 6-2 victory. The defending champs are trying to become the first men's double team of the Open era, and the first since 1951, to win all four major tournaments in the same year.
They've already achieved a "Bryan Slam'' with four straight titles starting with the 2012 U.S. Open.
Struggling with returning serve, the top-seeded Bryans switched sides after the opening set for the first time in about three years.
After going down a break at 3-4 in the second set, the American twins immediately broke back against the 40-year-old Nestor's serve. They clinched the set by breaking his serve again, with Nestor double-faulting twice in the game, including on match point.
The Bryans broke his serve twice more in the third set to advance.
- AP
