The Blues defeated Havdar 2-1 in Karaj, west of Tehran.
After 11 minutes into the match, Rudy Gestede found the back of the net from the penalty spot.
Mohammad Javad Mohammadi equalized the match in the 40th minute.
With six minutes remaining, Arsalan Motahari scored the winner with a header.
Siavash Yazdani was sent off in the 88th minute after receiving his second yellow card.
Esteghlal leads the table with 38 points, three points above its archrival Persepolis.