Iman Mobali found the back of the net from the penalty spot in the injury time of the first half.
In the heated encounter, referee Mo`ud Bonyadifar sent off Tohid Gholami in the 79th minute.
With four minutes remaining, the referee announced a controversial penalty for Sepahan after Sepahan player was brought down in Naft Tehran area.
Naft Tehran football coach Ali Daei was sent off after protesting to the referee decision.
Ehsan Haji Safi failed to score the penalty.
Shoja Khalilzadeh and Abbas Bouazar from Sepahan and Naft Tehran respectively were shown red cards due to head butting.
Naft Tehran will play the winner of Tractor Sazi and Zob Ahan match which has been scheduled on Saturday in Tabriz.