In the match held in Takhti Stadium in Jam, Saeid Mehri scored the winner for the visiting team in the 97th minute.
Havadar also defeated first-tier Esteghlal Mollasani 2-1 in Mollasani’s Shohada Stadium.
Mohammad Chaharmahali and Masoud Shojaei were on target for the visiting team and Mohammadamin Saeidavi scored Mollasani’s goal.
On Sunday, Persepolis will host Gol Gohar Sirjan in Tehran and Nassaji meet Paykan in Ghaemshahr.
Hazfi Cup is the Iranian football knockout cup competition, run by the Iranian Football Federation. Esteghlal are the most successful club with seven titles.
Nassaji Mazandaran are the titleholders.
MNA/TT