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World No.1 Iga Swiatek of Poland moved into the fourth round of the US Open on Sunday (IST) defeating American Lauren Davis 6-3, 6-4, keeping the two-time French Open champion on course for her maiden singles title at Flushing Meadows.

The top-ranked Swiatek was tested in the match but she stepped up during crucial moments to equal her best performance at the season-ending Grand Slam. The Pole had also reached the fourth round last year.

Swiatek, 21, is trying to become the first player since Serena Williams to win seven titles in a single year; the now-retired American having achieved the feat eight years ago, when she also became the last No.1 seed to take the US Open title.

Swiatek has played amazing tennis this year, with her 37-match winning streak earning her the French Open crown and WTA 1000s titles in Doha, Indian Wells, Miami and Rome.

"I could not find my rhythm today," Swiatek said about the tough match on Sunday. "She (Davis) played pretty smart. I'm pretty happy at the end that I could put balls in. I'm just trying to enjoy any match, even when I'm not perfect," Swaitek was quoted as saying by wtatennis.com.

The summer hard-court season, though, hasn't been that great for Swiatek, who has won just four of seven matches.

She came out firing against Davis, hitting nine winners, including two aces, in the first two games. The attacking game, combined her impeccable defence was too much for Davis to take in.

Swiatek thus remains undefeated against players ranked outside the top-100 in Grand Slam play (15-0). She's won 53 matches this season and is already closing in on the most recent standard, 57, set three years ago by Australia's Ashleigh Barty, according to WTA.

Swiatek, who became the No.1-ranked player in the world in April after Barty announced her shock retirement, complimented Serena Williams' staying power over the years in such a competitive environment.

"Being in this situation (for five months now), I know how tough it is sometimes to find balance and to actually stay focused on the proper things. I think she (Serena) did very well. I have huge appreciation because it's one of my goals actually to be consistent throughout my whole career, staying top-10 for a long, long time.

"She was No.1 for a long, long time, so it's pretty crazy. For sure, I understand it little bit more right now, how much work she has put into it," added Swiatek.

Swiatek will take on Germany's Jule Niemeier in the fourth round. A quarterfinalist at Wimbledon earlier in the summer, Niemeier defeated Zheng Qinwen 6-4, 7-6(5) to make the Round of 16 in her tournament debut.