The 25-year-old Pole beat Germany's Oscar Otte 6-4, 6-2, 6-4 in their first-round men's singles match at Flushing Meadows on Tuesday.
Hurkacz, who is 10th in the world ranking, next takes on Belarusian world No. 73 Ilya Ivashka for a place in the third round.
Poland’s world No. 1 in women's tennis, Iga Świątek, has also advanced to the second round of the US Open, where she will face home favourite Sloane Stephens.
Meanwhile, countrywoman Magda Linette crashed out in the first round of the Grand Slam tournament in New York after losing 2-6, 6-4, 6-7 to the Czech Republic's Karolina Plíšková on Tuesday.
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Source: PAP