Vouria Ghaffouri scored the only goal of the match in the 40th minute.
Persepolis managed to get more of the ball in the second half, although they failed to open Esteghlal’s goal.
Persepolis could win the IPL title with a draw because second-place Zob Ahan was held to a goalless draw against Pars Jonoubi.
Ghaffouri was named the Man of the Match.
Elsewhere, Paykan defeated Tractor Sazi 1-0 thanks to a goal from Mehdi Momeni.
Persepolis sits top of the IPL table with 57 points, followed by Zob Ahan (42) and Esteghlal (41).