The 24-year-old Pole beat Belarus' Egor Gerasimov 6-3, 6-4, 6-3 in their first-round men's singles match at Flushing Meadows on Tuesday.
Hurkacz, 13th in the world ranking, next takes on Italian world No. 89 Andreas Seppi for a place in the third round.
Poland’s 2020 Roland Garros champion Iga Świątek has also advanced to the second round of the US Open.
Meanwhile, Polish players Kamil Majchrzak and Magda Linette both crashed out in the first round of the Grand Slam tournament in New York.
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Source: PAP