In front of more than 80,000 fans in Tehran’s Azadi Stadium, Sajjad Shahbazzadeh found the back of the net with a spectacular long-range shot in the 33rd minute.
Two minutes before, Mohammad Ebrahimi had failed to put the visiting team the lead from the penalty spot.
Mohsen Karimi extended Esteghlal’s lead two minutes before the interval.
Gostaresh reduced to 10 men in the 58th minute after Mohammad Nosrati received a straight red card.
Gostaresh’s striker Shahram Goudarzi reduced the deficit in injury-time.
Elsewhere, Esteghlal Khuzestan was held to a 1-1 draw against Saba.
Karim Eslami was on target for Saba in the 47th minute and Farshad Janafza equalized the match in the 58th minute.
Struggling Esteghlal Ahvaz suffered a 1-0 home defeat to Naft Tehran, Malavan played out a goalless draw against Rah Ahan and Siahjamegan drew 1-1 with Padideh.