Majid Aliyari found the back of the net with a powerful shot into the area at the Shohada-ye Shahr-e Qods Stadium in the 56th minute.
Omid Latifi was on target in the 70th minute after escaping from an offside trap and Aliyari completed his brace in the 87th minute.
Esteghlal is 11th in the 16-team table with eight points out of seven matches and Zob Ahan moved up to seventh place with 10 points.
Esteghlal parted company with its head coach Javad Nekounam last month and is headed by interim coach Sohrab Bakhtiarizadeh.