The duo beat Serbia's Laslo Djere and Switzerland's Marc-Andrea Huesler 6-3, 7-6 in the second round at the weekend.
Up next for Zieliński and Nys at the Grand Slam tournament in New York is the Mexican-French duo of Santiago González and Édouard Roger-Vasselin.
Meanwhile, Poland's Magda Linette has booked her place in the third round 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 is set to take on Latvian Jelena Ostapenko for a place in the last eight of the women's singles 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.
Poland's world No. 77 Magdalena Fręch 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 at Flushing Meadows after being bested by Britain's Jack Draper in the second round.
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Source: IAR, PAP
