Linette and Pera beat American Nicole Melichar-Martinez and Australian Ellen Perez 6-3, 7-6 in the second round at Flushing Meadows at the weekend.
Up next for the Pole and the American at the Grand Slam tournament in New York is the all-American duo of Sophie Chang and Alycia Parks.
Meanwhile, Poland's Jan Zieliński has reached the third round of the US Open men's doubles, partnering with Hugo Nys of Monaco.
In the women's singles, Poland's world No. 1 Iga Świątek will take on Latvian Jelena Ostapenko for a place in the quarterfinals at the US Open.
Świątek is the last Pole still standing in the singles at this year's US Open, which runs until September 10.
Linette bowed out of the US Open women's singles in the second round after being eliminated by home favourite Jennifer Brady.
Poland's world No. 77 Magdalena Fręch, meanwhile, was ousted in the second round by Czech world No. 10 Karolína Muchová.
In the men's singles, Poland's 17th-seeded Hubert Hurkacz crashed out of the tournament after being bested by Britain's Jack Draper in the second round.
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Source: IAR, PAP