Midfielder Mohammad Nouri scored the Reds' solo 38 minutes into the match at Tehran's Azadi Stadium in the league's 16th week on Thursday.
30 minutes after the break, Bahador Abdi scored the equalizer to mark the 12th draw for Ali Daei's side.
Estili, himself a former Persepolis player, resigned last Friday over a 3-0 loss at the hands of archrival Esteqlal.
Elsewhere, in the west-central city of Qom, Saba was held to a 1-1 tie by Sepasi and Zob Ahan beat Mes 1-0 in the central city of Isfahan.
Esteqlal is now atop the table with 33 points followed by Naft Tehran with 30.