The 31-year-old Pole beat Belarusian Aliaksandra Sasnovich 6-3, 6-1 in the first round of the women's singles at Flushing Meadows.
Linette, 24th in the world ranking, next takes on American Jennifer Brady in the round of 64.
Poland’s world No. 1 Iga Świątek and 77th-ranked Magdalena Fręch have also advanced to the second round of the US Open.
On the men's side, Poland's Hubert Hurkacz is set to face Swiss player Marc-Andrea Hüsler in the first round of the Grand Slam tournament in New York on Tuesday.
(gs)
Source: PAP