Striker Hadi Norouzi broke the deadlock for Persepolis after 18 minutes, but the visitors equalised three minutes later through Mohammad Ahmadpouri.
Persepolis looked to have earned a third win of the new season when midfielder Karim Bagheri struck with two minutes remaining.
But Reza Bazyari netted a last-minute equaliser as basement side Shahin moved level on points with Foolad after six games. Persepolis crept up to seventh, three points behind early leaders Peykan - who recorded a fourth straight win when they edged out Steel Azin 1-0 on Sunday.