The 29-year-old Pole beat Latvia's Anastasija Sevastova 6-4, 7-5 in their first-round women's singles match at Melbourne Park on Tuesday.
Linette, 53rd in the world ranking, next takes on Russian world No. 25 Daria Kasatkina in the round of 64.
Magda Linette. Photo: PAP/EPA/NEIL HALL
Poland’s Iga Świątek, Hubert Hurkacz and Kamil Majchrzak have also advanced to the second round of the 2022 Australian Open.
Majchrzak, who is ranked world No. 107 by the Association of Tennis Professionals (ATP), on Tuesday overcame Italy's 101st-ranked Andreas Seppi 6-1, 6-1, 7-5.
Kamil Majchrzak. Photo: PAP/Leszek Szymański
Meanwhile, Polish player Magdalena Fręch crashed out in the first round of the Grand Slam tournament in Australia, losing to Romania's former world No. 1 Simona Halep, 4-6, 3-6.