The duo beat the Mexican-French pairing of Santiago González and Édouard Roger-Vasselin 6-7, 6-4, 6-2 in the third round on Monday.
Up next for Zieliński and Nys at the Grand Slam tournament in New York is the Croatian-American pairing of Ivan Dodig and Austin Krajicek.
Zieliński and Nys in May won the men’s doubles at the Italian Open clay-court tournament in Rome.
In January, the two reached the final of the Australian Open men's doubles in Melbourne.
Meanwhile, Poland's Magda Linette has booked her place in the quarterfinals of the US Open women's doubles competition, partnering with American Bernarda Pera.
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. 1 Iga Świątek, meanwhile, was ousted by Latvian Jelena Ostapenko in the last 16 of the women's singles at the US Open.
Świątek was the last Pole still standing in the singles at this year's US Open, which runs until September 10.
Poland's world No. 77 Magdalena Fręch was eliminated 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 at Flushing Meadows after being bested by Britain's Jack Draper in the second round.
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Source: IAR, PAP