Williams won eight of the last nine games to advance after 87 minutes to a last-eight matchup against Spanish 18th seed Carla Suarez Navarro, who upset German eighth seed Angelique Kerber 4-6, 6-3, 7-6 (7/3).

"It will be a tough match," Williams said. Williams, who at 31 could become the oldest US Open women's champion, and Stephens had not played since the 20-year-old prodigy beat the four-time US Open champion 3-6, 7-5, 6-4 in an Australian Open quarter-final last January.

"It definitely felt like a bigger match because Sloane is such a great player, but I had to stay focused in the moment," Williams said.

"I just tried the whole time to do what I wanted to, stay calm and stay relaxed."The Williams-Stephens relationship was strained after Stephens accused the 16-time Grand Slam champion of being disrespectful and using intimidation tactics and mind games with her yells of "Come on," but both women said before the match that soured feelings had been repaired.

In the match, both apologized to each other for wind-blown ball tosses that they did not hit. And when they met at the net after match point, Williams told Stephens, "I love you so much."

Stephens said she was simply outplayed by the world's best. "I thought I played good. I played pretty solid," Stephens said. "The second set got away from me a little bit.

"She's number one for a reason. She played pretty well herself. She did a lot of things well. All in all, she did great. I played well. That's all you can do."

The showdown of African-American stars, the world number one and the second-highest-rated American player, came in windy conditions at Arthur Ashe Stadium. Both wore expressions of stoic, grim determination during the match.