Reza Asadi gave the visiting team a lead in the 93rd minute but Kevin Yamga leveled the score from the penalty spot in the 110 minute.
The French striker was on target once again from the spot just before the final whistle.
Elsewhere, Mes Kerman defeated Sanat Naft 2-0.
Hazfi Cup is the Iranian football knockout cup competition, run by the Iranian Football Federation. Esteghal is the most successful club with seven titles.
Nassaji Mazandaran is the titleholder.