Iga Swiatek, of Poland, serves to Lauren Davis, of the United States, during the third round of the US Open tennis championships on Sept 3, 2022, in New York. (JASON DECROW / AP))

NEW YORK - World number one Iga Swiatek dug her way out of a second set hole to notch a 6-3 6-4 win over American Lauren Davis and reach the fourth round of the US Open for the second straight year.

Despite the deficit the feisty Iga Swiatek stubbornly refused to drop her first set of the US Open, winning a tense 16-shot rally to set up break points at 4-4, which she converted when Lauren Davis whacked a backhand into the net

The French Open champion came out sharp and fired an unreturnable serve out wide to capture the first set before falling behind 4-1 in the second as Davis raised her level.

Despite the deficit the feisty Pole stubbornly refused to drop her first set of the tournament, winning a tense 16-shot rally to set up break points at 4-4, which she converted when Davis whacked a backhand into the net.

In the end, Swiatek's superior serving and relentless defense carried the day against Davis, who plays a similar but less potent brand of tennis as Swiatek.

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The 21-year-old top seed admitted she was not at her best during the two-hour night match on Louis Armstrong Stadium despite reeling off the match's final five games.

Lauren Davis, of the United States, celebrates winning a point against Iga Swiatek, of Poland, during the third round of the U..Open tennis championships on Sept 3, 2022, in New York. (JASON DECROW / AP)

"I couldn't find my rhythm today," Swiatek said in an on-court interview.

"She played totally differently than any other player. She played very smart. I'm pretty happy at the end that I could put balls in.

Swiatek went on a blistering 37-match winning streak earlier this year to claim titles in Roland Garros, Doha, Indian Wells, Miami and Rome but cooled off this summer, losing four matches during the hard-court season

"I'm trying to enjoy every match even when it's not perfect. Just trying to go for it. Trying to find solutions in every situation."

Swiatek went on a blistering 37-match winning streak earlier this year to claim titles in Roland Garros, Doha, Indian Wells, Miami and Rome but cooled off this summer, losing four matches during the hard-court season.

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So far in New York she has put to rest any questions about her form and will be the heavy favourite when she takes on Germany's Jule Niemeier on Monday after the Wimbledon quarterfinalist upset China's Qinwen Zheng 6-4 7-6(5) to reach the Round of 16.