The 25-year-old Pole beat home favourite Emma Navarro 7-6, 1-6, 6-2 in their first-round women's singles match at Flushing Meadows on Monday.
Fręch, who is 77th in the world ranking, next takes on Czech world No. 10 Karolína Muchová for a place in the third round.
Poland’s world No. 1 Iga Świątek on Monday eased past Sweden's Rebecca Peterson 6-0, 6-1 in the first round of the women's singles at the Grand Slam tournament in New York.
Świątek, who is the defending champion in New York, will face Australian Daria Saville in the second round.
The 2023 US Open began on Monday and runs until September 10.
(gs)
Source: Eurosport, IAR, PAP