By Larry Fine

NEW YORK (Reuters) - World number one Caroline Wozniacki was two games away from being dismissed by former champion Svetlana Kuznetsova in straight sets before roaring back to reach the quarter-finals of the U.S. Open Monday.

The 15th-seeded Kuznetsova, the 2004 winner, won six of the last seven points of their first-set tiebreaker and led 4-1 in the second set before the Danish top seed recovered for a 6-7 7-5 6-1 win under the lights at Arthur Ashe Stadium.

"It was a tough match. A good battle," Wozniacki said.

Wozniacki, 21, executed the turnaround after reminding herself of their last U.S. Open encounter in 2009 when she dug out of a similar hole and blazed back for victory.

"The last time I played her here, it was fourth-round as well, night session, and I lost the first set and was down I think 3-0 and, 4-1 in the second.

"I fought back and I won. So I said: 'I can do this. I just have to keep playing for every point.' I just kept fighting."

Wozniacki won the 2009 match in a third-set tiebreaker and went on to reach the finals before falling to Kim Clijsters.

This time, she made it easier on herself by winning 12 of the last 14 games to book her place in the quarters, where she will meet 10th seeded Andrea Petkovic of Germany, a 6-1 6-4 winner against unseeded Carla Suarez Navarro of Spain.

Kuznetsova, 26, controlled the action early going for winners to shorten points against the steady groundstroker.

Midway through the second set, the Russian grew exhausted and sprayed mis-hits all over the court. She finished the three-hour match with a remarkable 78 unforced errors, three times more than the Dane.

"I had chances," said Kuznetsova, who also won the 2009 French Open. "I missed the chances.

"Yes, I did lots of unforced errors, but because I was trying to come very aggressive and to dictate and I was doing this.

"She was a wall, you know," added the Russian about Wozniacki's ability to retrieve shots.

Wozniacki broke the Russian's serve four times in a row to charge back in the second set and claim a 2-0 lead in the third on her way to victory.

"After two sets I still felt fresh," said Wozniacki, one of the fittest players on the women's tour and the winner of six tournaments this year.

"I know that I'm in good shape and can play out there for five hours if I have to. I'm very proud of what I achieved today."

(Reporting by Larry Fine; Editing by John O'Brien)