Left winger Mohsen Yousefi scored the goal of the day after 17 minutes, when he beat the offside after a nice chip from Jlloyd Samuel and made no mistake from close range.
Iranian national team keeper Mehdi Rahmati brilliantly saved two dangerous efforts at the hourmark.
Rahmati became the match winner, when he stopped another 100%er from Malavan striker Jalal Rafkhaei after 75 minutes.
On the other side, Esteghlal's Milad Meydavoudi beat the goalkeeper, but was denied by the goalpost whereas Arash Borhani's effort was cleared off the line by a defender.
Thanks to the win, Esteghlal remain in third position of the league table, on equal points with second placed Tractor Sazi Tabriz, but were able to reduce the gap to leaders Sepahan to three points.