NEW YORK, USA (AFP) — Top-ranked defending champion Serena Williams defeated US 15th seed Sloane Stephens 6-4, 6-1 yesterday to reach the US Open quarter-finals, avenging a loss that ousted her from the 2013 Australian Open.

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 apologised 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.

Red-dressed Williams was thwarted on three early break points against purple-clad Stephens, but finally broke through for a 4-2 lead with a forehand service winner return that prompted a quick fist pump from the top seed.

But Williams surrendered a break on a double fault in the next game and Stephens held to level the first set at 4-4, saving a break point with a forehand winner in the process.

Williams held and then broke to win the inaugural set after 52 minutes, finding success on her third break chance in an 18-point game when Stephens swatted a forehand wide.

Stephens forced a break point in the opening game of the second set, but Williams saved it with a forehand winner and went on to hold.

Williams finished off a love service third game with a winner that hit Stephens at the baseline and elicited a squeal but no further reaction.

Williams broke for a 3-1 lead when Stephens netted a baseline forehand, the defending champion yelling “Come on” and pumping her fist with delight, then held serve at love for a 4-1 advantage, broke again and ended the match by holding when Stephens netted a forehand.