Shpetim Arfi opened the score line in the 12th minute, heading home a cross by Hadi Nowruzi.
Nine minutes later, Bahman Tahmasbi converted a controversial penalty for Naft to set things level.
After conceding the equalizer, the Reds created numerous chances and dominated the possession.
Persepolis' best opportunity to retake the lead came in the 41st minute when Hossein Badamaki fired a shot from within the 18-yard-box. His shot, however, was deflected by Naft outfitted defenders.
Six minutes into the second half, out-of-favor Arfi scored his second goal of the game to prove his abilities to Persepolis Manager Ali Daei.
Eight minutes from time Ali-Reza Nour-Mohammadi headed home from a corner to seal the victory for the Reds.
Also on Friday, Amin Motevasselzadeh, Iman Razaqi and Bahado Abdi scored for Rah Ahan to defeat Steel Azin 3-0 at Ekbatan Stadium.
With 27 points, Persepolis now trails league leader Zobahan by a single point. Archrival Esteqlal stands third with 24 points after conceding a 2-0 defeat against Sanaat Naft Abadan on Thursday.