Ahmad Nourollahi scored the winning goal for Persepolis in the 21st minute from a corner kick.
Esteghlal missed a golden chance to equalize the match in the last minute of the first half but Farshid Esmaili failed to score from the penalty spot.
Esteghlal leads the head to head results in competitive matches with 26 wins to Persepolis's 24, while 40 matches ended in a draw.
Tehran derby is a football match between the two prominent Tehran clubs Esteghlal (Blues) and Persepolis (Reds).
Persepolis moved five points clear at the top of the IPL table.
