In the match held in Kerman, Moein Abbasian gave the lead the host in the 10th minute but Milad Khodaei scored an own goal nine minutes later.
Jafar Salmani and Mehdi Ghaedi scored two goals for Esteghlal in the 70th and 73rd minutes.
Mes Kerman player Aref Rostami scored a consolation goal in the dying moments of the match.
In Abadan, struggling Sanat Naft lost to Havadar 1-0, Mes Rafsanjan was held to a goalless draw by Zob Ahan and Paykan and Naft Masjed Soleyman played out a goalless draw.
Esteghlal moved to third place, three points behind Sepahan and Persepolis.