Taking eight of the last nine games, defending champion Williams returned to the quarterfinals at Flushing Meadows, beating Stephens 6-4, 6-1.
Still for eight games Stephens stayed right with Williams, topping 115 mph serves much like the U.S. Open women’s champion.
And for 40-minute stretch in the fourth round of the US Open, the top two American women put on quite a show. But at the end of it, Stephens, 20, failed to get the better of Williams, 31.
“When you give her that opportunity to take that step forward, she definitely makes her move,” Stephens said after the match. “Unfortunately, today she made her move. I just couldn’t get back in.”
As for Williams she is elated. “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 will now play No. 18 Carla Suarez Navarro of Spain, who defeated No. 8 Angelique Kerber of Germany 4-6, 6-3, 7-6 (3).
Meanwhile, in other U.S. Open results, Andy Murray dispatched German Florian Mayer 7-6 6-2 6-2 to move into the fourth round.
And Camila Giorgi beat No 1 Caroline Wozniacki 4-6, 6-4, 6-3 in the third round of the U.S. Open on Saturday, Aug. 31.