Persepolis young striker Mehdi Abdi found the back of the net in the 29th minute.
Persepolis could have scored the second goal in the second half but Ehsan Pahlevan wasted his chance.
Just after the hour mark, the referee showed the penalty spot after a handball from Persepolis defender Hossein Kanaani.
Foolad Brazilian forward Luciano Pereira converted the penalty.
With 13 minutes left on the clock, Ahmad Nourollahi scored for Persepolis from a set-piece.
Earleier in the day, Esteghlal had defeated Tractor 3-1 in Tabriz to move top of the table.