They were evenly matched for much of the first set at Arthur Ashe Stadium.
Williams blasted an ace out wide to start the proceedings and held serve at love.
Stephens replied with a tougher fought but impressive hold, easily handling Williams’s vaunted power and winning a 23-stroke rally.
While Williams held serve with ease, Stephens made her own statement of strength in fighting so hard to hold her serve in reply. She made Williams work on each rally, yanking her from side to side with sharply angled forehand blasts.
Serving at 4-5, Stephens fended off two set points before getting broken to lose the set.
Facing break point in the opening game of the second set, Williams uncorked two huge serves to dig out of trouble. Then she broke Stephens in the fourth game by playing terrific defense to take a 3-1 lead, then erupted with a huge “C’mon!” and fist pump.
Williams cruised from there as Stephens started over-hitting in an effort to stay in the match.
After Stephens’s final forehand plowed into the net to end the match, they met at the net and clasped hands. Moments later, Williams praised Stephens once more during an on-court interview broadcast to the crowd.
“Sloane is such a great player!” Williams said. “How excited are we for the future of American tennis, right?”
Indeed, Stephens did so many things right. She had no trouble with the pace of Williams’s serve. She played the aggressor at key moments. She ripped her forehand with authority. And she seemed the fitter woman, barely breathing hard after furious rallies.
But with her occasional wild shots, whether struck off balance or overly aggressive, she also demonstrated that the future of American tennis needs a bit more incubation time.
Notes: Earlier Sunday, defending U.S. Open men’s champion Andy Murray needed less than two hours to dispatch Germany’s Florian Mayer, 7-6 (7-2), 6-2, 6-2.
Top seed Novak Djokovic needed even less time against Joao Sousa of Portugal, advancing, 6-0, 6-2, 6-2, in 1 hour 41 minutes.
The women’s draw lost No. 3 seed Agnieszka Radwanksa, who was ousted by Ekaterina Makarova, 6-4, 6-4. And No. 5 Li Na dismantled Jelena Jankovic, 6-3, 6-0.
The top-ranked doubles team of Bob and Mike Bryan survived a scare but advanced to the quarterfinals upon defeating the unseeded tandem of Canadians Daniel Nestor and Vasek Pospisil, 6-7 (7-1), 7-5, 6-2.
The 35-year-old twins, who have won 15 major titles, are trying to become the first men’s doubles team in 62 years to win all four majors in the same year.