Zob Ahan survived the first-half sending-off of Shahin Kheiri as Seyed Mohammad Hosseini gave them the lead on the stroke of half-time.
Muhammad Salsali's 80th-minute strike moved them two points behind Sepahan having played a game more. Shahrdari, for whom Saeid Daghighi pulled a goal back with a late penalty, remain 12th, but are still not clear of the relegation battle.
Esteghlal moved within three points of the leaders with a 1-0 win at rock bottom Rah Ahan, the goal coming from Hawar Mulla Mohammad.
The win also moves Esteghlal five points clear of fourth placed Tractor, seemingly making the title fight a three-way fight.