Top seed Serena Williams reached the US Open quarter-finals with a 6-4 6-1 win over fellow American Sloane Stephens.

Stephens had knocked Williams out of the Australian Open when the pair met in Melbourne at the start of the year and again had her moments during a tight opening set in New York.

But defending champion Williams gained the crucial break in the 10th game, when the 20-year-old Stephens double faulted twice as she served to stay in the opening set.

And from there it was one-way traffic, Williams racing through the second set for the loss of just one game, completing victory in one hour and 27 minutes.

Williams admitted: "She's definitely a good player, so it felt like something bigger, but I just had to stay focused for the moment."

The 31-year-old Williams, who won eight of the last nine games, added: "The whole time I just tried to do what I wanted.

"Stay calm, stay relaxed, stay composed."

A beaten Stephens said: "Obviously, she's No 1 in the world for a reason. 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 now faces Carla Suarez Navarro in the last eight after the Spaniard stunned eighth seed Angelique Kerber of Germany 4-6 6-3 7-6 (7/3).