The 25-year-old Pole beat Italy's Giulio Zeppieri 7-5, 6-2, 7-5 in their first-round men's singles match at the Grand Slam tournament in the French capital on Tuesday.
Hurkacz, 13th in the world ranking, next takes on Italian world No. 132 Marco Cecchinato for a place in the third round.
Poland’s 2020 Roland Garros champion Iga Świątek and countrywoman Magda Linette have also advanced to the second round of the French Open.
Meanwhile, Polish players Kamil Majchrzak and Magdalena Fręch crashed out in the first round of the singles competitions at the Grand Slam tournament in Paris.
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Source: PAP