Alireza Koushki scored the only goal of the match for Esteghlal at the minute of 56 through a header.
The coachless Tehranian team moved up to the seventh place in the PGPL table after the narrow win with 26 points.
Tractor Sazi lead Iranian professional league with 44 points, followed by Sepahan with 43 points.
Nassaji are in the 15th place at the 16-team table after today's defeat.
MNA