The duo beat Spaniards Pedro Martínez and Jaume Munar 7-6, 7-5 in the first round on Thursday.
Up next for Zieliński and Nys at the Grand Slam tournament in New York is the Portuguese duo of Nuno Borges and Francisco Cabral.
Earlier on Thursday, Zieliński booked his place in the last 16 of the US Open mixed doubles, partnering with Hsieh Su-wei of Taiwan.
Meanwhile, Poland's Magda Linette and Alicja Rosolska have both advanced to the second round of the US Open women's doubles, each paired with an American partner. Linette is teaming up with Peyton Stearns, while Rosolska is playing alongside Catherine Harrison.
Linette's hopes for success at Flushing Meadows now rest on the doubles after she was ousted from the singles in the first round by home favourite Iva Jovic.
World No. 1 Iga Świątek is the last Pole still standing in the singles at this year's US Open, which runs until September 9.
Świątek is set to take on Russia's Anastasia Pavlyuchenkova for a place in the last 16 of the women's singles on Saturday.
In the men's singles, Poland's seventh-seeded Hubert Hurkacz crashed out of the tournament after being eliminated by Australia's Jordan Thompson in the second round on Thursday.
(gs)
Source: IAR, PAP
