Updated

By Steve Ginsburg

NEW YORK (Reuters) - World number one Caroline Wozniacki breezed into the fourth round of the U.S. Open with a methodical 6-2 6-4 victory over unseeded Vania King on a sunny day at the National Tennis Center on Saturday.

Wozniacki faced frequent trouble on her serve and was broken three times by the diminutive American during the one-hour 36-minute slugfest at Arthur Ashe Stadium.

"It was quite windy out there, so it was difficult to play," said Wozniacki, who failed to fire an ace and had three double faults.

"Definitely the serve was difficult because it wasn't going one way, the wind, it was going everywhere. You had to keep the margin over the net and from the lines."

King, ranked 103 in the world, broke Wozniacki's serve in the opening game of the match but midway through the set she began to spray the ball around and her game unraveled.

"It's a pity," said King. "I had a lot of chances in the first (set), a lot of breakpoint chances. She was a little bit more aggressive than I was and obviously she's one of the best players out there.

"So I needed to step it up when I needed to, and she did it a little bit better than me today."

The 22-year-old King rallied from 2-5 to 4-5 in the second set but then lost her serve to end the match.

"I found it difficult to place the ball so quite a few times I was going for the safe serve," said Wozniacki, who said she figured out her kick serve was a better way to attack.

"She liked it when I was going flat and she could just put the racquet on it and place it. I was trying to do a bit more, put it a bit more high over the net and try to get out of her strike zone."

In the round of 16 Wozniacki will face either 15th-seeded Russian Svetlana Kuznetsova, the 2004 champion, or Akgul Amanmuradova of Uzbekistan.

"I've been playing pretty well the last two weeks," said Wozniacki. "I won New Haven and I've made the fourth round now. "I feel like my game is on the right track."

King, who is playing doubles and mixed doubles, admitted she ran out of gas against Wozniacki.

"Obviously I have to get fitter because this is the third round and you never know how you're going to do," she said. "I felt like I had two really solid matches before this, but yesterday I had doubles and mixed.

"To be honest, if I had known I would do so well in singles I would have re-thought the mixed."

(Editing by Larry Fine)