The hosts had taken the lead through Mohammad Nouri after 15 minutes and looked set to take all three points only for Mehdi Agha Mohammadi to equalise in stoppage time.
The draw means Perspolis trail Zob Ahan by two points after eight games.
Meanwhile, a fifth-minute strike from Mohsen Bayat secured a 1-0 win for Saba Battery over Steel Azin.
The victory means Saba move up to fifth in the standings.
In other games, Sepahan edged Shahrdari Tabriz 1-0 and strugglers Rah Ahan beat Malavan 2-0.
