The Blues, who sought the first win at home, lost many opportunities to end the first half with a goalless draw at Tehran's Azadi Stadium on Wednesday night.
However, the home side took the lead in the second half when defender Pejman Montazeri took advantage of Peykan goalkeeper Ebrahim Mirzapour's blunder and opened the scoring in the 60th minute.
The 25-year-old striker Milad Meidavoudi struck a wonderful free-kick just four minutes later to keep the Blues in the race for the IPL title.
Esteqlal skipper Farhad Majidi sealed the victory twelve minutes from time to send cheers to thousands of his team's fans at the sporting venue.
Esteqlal manager Parviz Mazloumi voiced satisfaction with the decisive victory and said the team was nearing an "ideal situation" day by day.
However, Peykan's boss, Mohammad Ahmadzadeh, said his team did not deserve "such a heavy defeat at all."
"Esteqlal is a big team but it achieved the victory only due to Peykan players' mistakes," he went on to say.
The win moves Esteqlal to the sixth place in the IPL table with 8 points. Zob Ahan, under Mansour Ebrahimzadeh, tops the standings on 13 points after five games, followed by Pas with 10 points. Steel Azin, coached by Serbian Ljubisa Tumbakovic, sits third on 9 points.
Other Wednesday match results:
Shahin 0-0 Teraktorsazi
Zob Ahan 1-0 Sepahan
Steel Azin 1-1 Mes
Pas Hamedan 1-1 Sanaat Naft
Saipa 3-2 Malavan