NEW YORK // Serena Williams, the defending champion, won her much-anticipated US Open showdown with Sloane Stephens on Sunday while Li Na avenged a painful loss in Rome to join the world No 1 in the last eight.
Williams defeated Stephens, the US 15th seed, 6-4, 6-1 to reach the US Open quarter-finals, winning eight of the last nine game in avenging a loss that ousted her from the 2013 Australian Open.
"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."
Williams booked a quarter-final against Spanish 18th seed Carla Suarez Navarro, who upset German eighth seed Angelique Kerber 4-6, 6-3, 7-6.
Also booking a quarter-final match-up were Chinese fifth seed Li, who beat Serbian ninth seed Jelena Jankovic 6-3, 6-0, and Russian 24th seed Ekaterina Makarova, who upset Polish third seed Agnieszka Radwanska 6-4, 6-4.
Li, the 2011 French Open champion, matched her best US Open result by reaching the last eight.
"Maybe today was the best match of my whole life," Li said, saying that her strategy against Makarova would be to "play aggressive".
"I wish I can play the same level like today," she added.
Li improved to 5-4 against Jankovic, motivated by the sting of a loss in their most recent match in a round-of-16 affair last May in Rome.
"Last time I lost to her in Rome I was feeling so sad," Li said. "I was feeling I played so good. I said, 'You have to remember how you felt after Rome and not have that feeling any more.'"
Suarez Navarro hit 45 winners and took advantage of 50 unforced errors by Kerber to rally for the victory after two hours and 41 minutes.
Radwanska dropped the last eight games and was ousted in the fourth round at the US Open for the fourth time, having never reached the quarter-finals.
"I want to know as well what happened," Radwanska said. "She was a little nervous in the beginning and she started playing better and better and I didn't do anything to win that first set."
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.
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 87-minute 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 No 1 for a reason. She played pretty well herself. She did a lot of things well."
The showdown of African-American stars, the world No 1 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.
"It was a high-quality match," Williams said. "I was really focused. I just tried to be positive a lot on my serve. My defense was good. I generally have been playing better defense this year, moving better and trying to be faster."
Stephens set a goal of trying to crack the season-ending top 10, a move made easier because she has no points to defend the rest of the year.
"Obviously I want to keep getting better, just little things I can do to keep improving to get to the next level," Stephens said.
"I'm going to try and break into the top 10 at the end of the season. That's a big jump from where I was last year, around 40 and kind of lingering. This year has been pretty good year for me. I'm going to try to end it with a bang."
Williams did say Stephens got one thing wrong, however: "She's already at the next level."
Big win for Djokovic
Top seed Novak Djokovic roared into the fourth round with a 6-0, 6-2, 6-2 victory over Joao Sousa of Portugal under the lights of Arthur Ashe Stadium on Sunday.
The 26-year-old Serb, who has yet to lose a set, smacked 34 winners to just 10 for the 95th-ranked Sousa in the 100-minute rout.
Djokovic, the Australian Open champion, faced just two break points in the match leading to one service break, while converting eight of 13 against his opponent.
Djokovic said his top priority was winning as quickly as possible, but found some time to fine-tune his net game.
"I am not obviously as comfortable on the net as I am on the baseline, but I've been working on it," said the world No 1, who won 22 of 30 points he contested at the net.
"It's part of my game that I still need to improve. I'm aware of that."
Djokovic said he was also putting in extra time with his serve.
"It makes me happy that I have room for improvement, and I keep on spending hours and hours on the court and working on variety in my game," he said.
"And serve, especially that part of my game. I want to try and get as many free points on the serve as possible."
Djokovic, a 2011 winner at Flushing Meadows who fell to Andy Murray in five sets in last year's final, next faces 43rd-ranked Marcel Granollers of Spain.
Murray progresses
Andy Murray, who ended his country's 76-year wait for a grand slam men's champion when he won his maiden major title in New York last year, eased past Germany's world No 49 Florian Mayer, 7-6, 6-2, 6-2.
His win was built on an impressive 42 winners and seven aces.
"I think I need to start my matches quicker than I have been doing. I am not that fast out of the blocks," said the 26 year old. "But once I got going I was striking the ball cleanly."
Murray, the reigning Olympic and Wimbledon champion, will next face Uzbekistan's world number 65 Denis Istomin, who put out Italian 20th seed Andreas Seppi, 6-3, 6-4, 2-6, 3-6, 6-1.
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