The 27-year-old Pole, ranked world No. 9 by the Association of Tennis Professionals (ATP), defeated British player Jack Draper 6-1, 7-5 in the round of 64 on Friday.
Hurkacz, who had a bye in the first round, will next face Germany's Daniel Altmaier at the clay-court tournament in the Spanish capital.
The Polish player is looking to improve on his performance at last year's Madrid Open, where he was eliminated in the third round by Croatia's Borna Ćorić.
Meanwhile, Poland's Iga Świątek has advanced to the third round of the women's singles at the 2024 Madrid Open, with a 6-1, 6-4 win on Thursday over China's Wang Xiyu.
The Polish world No. 1 will now play Romanian Sorana Cîrstea for a place in the quarterfinals.
The 2024 Madrid Open runs until May 5.
(gs)
Source: PAP