Iga Swiatek, of Poland, returns a shot to Daria Saville, of Australia, during the second round of the US Open tennis championships, on Aug 30, 2023, in New York. (PHOTO / AP)

NEW YORK - World number one Iga Swiatek moved into the third round of the US Open on Wednesday but not without a fight, taming feisty Daria Saville, who had warned she had the game to make the defending champion uncomfortable.

After a 6-0 6-1 rout of Sweden's Rebecca Peterson in her opening match, Swiatek did not look as at ease as she was made to work for a 6-3 6-4 win over the 322nd-ranked Australian spark plug.

"I just felt like I kind of prevailed, because that match wasn't easy," said Swiatek, who next meets the player she describes as her best friend on the WTA Tour Slovenian qualifier Kaja Juvan. "I'm just happy to be in the third round.

"For sure I want to improve some stuff, because I did some unforced errors.

Believing she could get into Iga Swiatek's head and possessed the type of game that could give her opponent trouble, Daria Saville did just that in an uneven opening set

"It's just the beginning of the tournament, so for sure I work on some stuff."

Saville had also impressed in her opener, sweeping past 17-year-old American Clervie Ngounoue 6-0 6-2 but the four-time Grand Slam winner represented a major step up in quality she could not match.

Believing she could get into Swiatek's head and possessed the type of game that could give her opponent trouble, Saville did just that in an uneven opening set.

Saville, who has only once before beaten a world number one, seven years ago against Angelique Kerber, got the match off to the best possible start breaking Swiatek at the first opportunity.

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Daria Saville of Australia returns a shot against Iga Swiatek of Poland during their Women's Singles Second Round match on Day Three of the 2023 US Open at the USTA Billie Jean King National Tennis Center on Aug 30, 2023 in the Flushing neighborhood of the Queens borough of New York City. (PHOTO / AFP)

But Swiatek would immediately break back when the Australian gifted her the first of six double faults in the opening set.

They traded breaks a second time before Swiatek would get her third of the set and hold serve for a 1-0 lead.

For sure I wanted to be intense and mostly I was in charge of what I'm going to kind of play, because I was the one that was attacking ... But for sure I made some mistakes because you kind of need to risk a little bit more.

Iga Swiatek, Polish professional tennis player

The two players continued to swap breaks in the second before the Pole went in front to stay with another break at 3-2.

But Saville would not wave the white flag, fist pumping after every big point, urging the Louis Armstrong crowd to get behind her.

"For sure I wanted to be intense and mostly I was in charge of what I'm going to kind of play, because I was the one that was attacking," said Swiatek. "But for sure I made some mistakes because you kind of need to risk a little bit more.

"She was using most of my power to get these balls back, I'm just happy at the end I was the one that won."

For Swiatek the win was another step towards defending her US Open crown and keeping the number one world ranking.

Despite having won four titles already this season, including the French Open for a third time, Swiatek's hold on the number one spot is under threat from Aryna Sabalenka, who is seeded second for the season's final Grand Slam.

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In order to remain in top spot Swiatek must go one round further than the Belarusian in Flushing Meadows.