Świątek advanced after beating America's 62-ranked Danielle Collins 6-4, 3-6, 6-4 in Round 2 (Round of 64) on Thursday.
Poland's world No. 1 will now face Linda Noskova of the Czech Republic for a place in Round 4 (Round of 16) of the first Grand Slam event of the year.
Poland's 69-ranked Magdalena Fręch progressed to Round 3 on Wednesday, while the 9-ranked Hubert Hurkacz was due to play his Round 2 match against Jiri Mensik of the Czech Republic later on Thursday.
Poland's Athlete of the Year Świątek reached the semi-finals of Australian Open in 2022.
The 2024 Australian Open tournament runs on the hard courts of Melbourne Park until January 28.
Source: polskieradio24.pl, WTA