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Serena Williams last won the US Open singles title in 2014

2018 US Open Venue: Flushing Meadows, New York Dates: 27 August-9 September Coverage: Live radio coverage on BBC Radio 5 live sports extra; live text commentaries on the BBC Sport website

Six-time winner Serena Williams reached the US Open quarter-finals with a 6-0 4-6 6-3 victory over Kaia Kanepi.

Williams, 36, took the first set in only 18 minutes as she converted all three break points she earned and did not drop a point on her first serve.

But Estonia's Kanepi responded, displaying some of the shot-making that helped her beat world number one Simona Halep in the first round.

Williams broke early in the third set as she completed her win in 97 minutes.

The 23-time Grand Slam singles champion will now play Czech eighth seed Karolina Pliskova.

And the American warned her rivals that her fitness has improved since reaching the Wimbledon final in July. She returned to competitive tennis in March after a year out during which she gave birth to her first child.

"It wasn't an easy match at all," said Williams, who last won the US Open title in 2014. "Kaia knows how to play and has a lot of big wins. She has had a great career.

"We always have tough matches, so I am just happy to get through. She was hitting such big returns so I wanted to hit bigger second serves.

"I like it when players challenge me to do that. I think what I have improved most is my fitness. Coming back from having a baby is really hard."

Williams tears Kanepi apart in first set

Williams dropped a set for the first time at this year's US Open

Williams produced a near perfect set - taking it 6-0 in 18 minutes which contained four aces, points won on every one of her successful first serves, three breaks from three chances and 14 winners.

"The 14 winners and two unforced errors was unreal, considering how big she was hitting the ball," former world number six Chanda Rubin told BBC Radio 5 live sports extra.

"We've been waiting to see Serena at the level she was at before her pregnancy.

"She still hasn't played many tournaments yet, but her level is there."

Kanepi responded brilliantly in the second set by breaking Williams twice before she held serve in the 10th game to level the match. It was the first set she had taken off the American in five meetings.

That setback prompted Williams to raise her level in the deciding set. The former world number one broke the world number 44 to go 2-0 up before sealing victory with a forehand winner in the ninth game.

Easy path for Williams?

With Halep, number two seed Caroline Wozniacki and Wimbledon champion Angelique Kerber having already fallen, few major obstacles stand between Williams and a seventh title in New York.

If she defeats Pliskova she could face defending champion and fellow American Sloane Stephens in the last four. Then there is the prospect of playing long-time rival Maria Sharapova in Saturday's final.