Mehdi Torabi found the back of the net from the penalty spot in the 31st minute and Isa Alekasir made the scoreboard 2-0 in the 45th minute in Tehran’s Azadi Stadium.
Gol Gohar winger Reza Shekari pulled a goal back in the 52nd minute.
Earlier in the day, Nassaji beat Paykan 3-0 courtesy of goals from Hamed Shiri, Behrouz Norouzifard (own goal) and Reza Jafari.
Esteghlal and Havadar have previously booked their place in the semifinals.
Hazfi Cup is the Iranian football knockout cup competition, run by the Iranian Football Federation.
Esteghlal is the most successful club with seven titles.