In the match, held in Arak’s Imam Khomeini Stadium, Saeid Mehri, who came off the bench, was tripped by Ramin Rezaeian in the 90th minute.
Hossein Kanaanizadegn found the back of the net from the penalty spot in the injury time.
Persepolis moved up to second place with 11 points out of five matches, while Esteghlal is ninth in the table with five points.
Out of 104 matches between the two teams, 50 have ended in draws so far, with Persepolis winning 28 and Esteghlal 26.