Esteghlal’s Arash Borhani put the visiting team in the 18th minute and Captain Farhad Majidi doubled the lead in 39th minute.
With three minutes remaining, Mehrdad Ghanbari pulled a goal back for Shahrdari.
Elsewhere, Saba lost to Damash 1-0 in a home game and Naft was defeated by Sanat Naft 3-1.
Esteghlal maintained its leadership of the IPL table with 33 points, followed by Traktorsazi, Naft and Saba with 27 points each.
