NEW YORK - Serena Williams easily won her eagerly-awaited clash with Sloane Stephens at the US Open on Sunday as normal service resumed at the last grand slam of year.

Williams was one of four US Open champions that won on Sunday, sending a clear message to the next generation's finest that they will have to wait their turn.

The 31-year-old avenged her loss to Stephens at the Australian Open with an emphatic 6-4 6-1 victory to keep her title defence on course.

"It's definitely difficult, especially playing people that you like, that you always want to see do well," Williams said.

Serena Williams of the US reaches for a return to compatriot Sloane Stephens at the US Open tennis championships in New York, Sept 1, 2013. [Photo/Agencies]

"But you have to go out there and kind of put that to the side and realize, I want to do well myself and take every point as it comes."

Stephens beat Williams in January in the quarterfinals at Melbourne Park to enhance her standing as a future leader of US women's tennis, but was completed outgunned by a woman bidding to become the oldest to win the US Open since tennis turned professional in 1968.

"Obviously she's number one in the world for a reason," said Stephens, 11 years younger than Williams. "I thought she played really well.

"All in all I thought I competed well and played well. That's all you can do really."

Williams will play Carla Suarez Navarro in the quarterfinals, the Spaniard having upset Germany's eighth-seed Angelique Kerber 4-6 6-3 7-6(3).

Sloane Stephens of the US serves to compatriot Serena Williams at the US Open tennis championships in New York September 1, 2013. [Photo/Agencies]