In the match, held at the Takhti Stadium in Khorramabad, Mehrdad Ghanbari gave the host a lead in the 10th minute. But Ramin Rezaeian equalized the match in the 55th minute.
Masoud Mohebbi made it 2-1 before the hour mark and Mohsen Sefid Choghaei was on target in the stoppage time.
Esteghlal has recently hired South African coach Pitso Mosimane.
It was the Blues’ fourth loss in eight matches.