NEW YORK (AP) -- For eight intense, entertaining games, Sloane Stephens stayed right with Serena Williams.
For a 40-minute stretch in the fourth round of the U.S. Open, the top two American women put on quite a show.
Both hit serves topping 115 mph. Both whipped groundstrokes to the corners.
Both covered a lot of ground, extending points with leg-churning defense. Both showed the occasional sign of nerves, reflecting what a big deal this was, in part because the 15th-seeded Stephens already was one of only three players to beat No. 1 Williams this season.
Until, that is, the score was 4-all in the first set Sunday. That's when Williams took over.
The 20-year-old Stephens' time at the top of tennis may come. For now, the 31-year-old Williams is still as good as it gets. Taking eight of the last nine games, defending champion Williams returned to the quarterfinals at Flushing Meadows by beating Stephens 6-4, 6-1.
"When you give her that opportunity to take that step forward, she definitely makes her move," Stephens said. "Unfortunately, today she made her move. I just couldn't get back in."
Still, all in all, it was remarkably compelling and, within individual points, rather evenly played for what turned out to be such a runaway.
"I definitely think it was a high-quality match," said Williams, 64-4 with eight titles this year. "We both came out today to play."
She advanced to play No. 18 Carla Suarez Navarro of Spain, who defeated No. 8 Angelique Kerber of Germany 4-6, 6-3, 7-6 (3). Asked whether there's any chance of a letdown after getting past Stephens, Williams replied: "Absolutely not. I mean, I've been at this for a long time, so for me in my career, there are no letdowns."
In Sunday's other fourth-round women's matches, No. 3 Agnieszka Radwanska lost 6-4, 6-4 to No. 24 Ekaterina Makarova, and 2011 French Open champion Li Na eliminated 2008 U.S. Open runner-up Jelena Jankovic 6-3, 6-0.
In men's third-round action, the last of 15 Americans in the field lost, making this the first U.S. Open in history without at least one representative from the host country in the fourth round. Wild-card recipient Tim Smyczek, who is ranked 109th, was beaten 6-4, 4-6, 0-6, 6-3, 7-5 by Marcel Granollers of Spain.