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.

“For sure it wasn’t easy, the rhythm of the match was weird,” said Swiatek.

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 No 1, seven years ago against Angelique Kerber, got the match off to the best possible start breaking Swiatek at the first opportunity.

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.

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 Swiatek the win was another step towards defending her US Open crown and keeping the No 1 world ranking.

Despite having won four titles already this season, including the French Open for a third time, Swiatek’s hold on the No 1 spot is under threat from Aryna Sabalenka, who is seeded second for the season’s final Grand Slam.

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