With just 10 minutes into the match, Nigerian striker Godwin Mensha scored and Ali Alipour made it 2-0 three minutes later.
Mehdi Shiri reduced the deficit in the 59th minute but Alipour scored in the 83rd minute to seal a 3-1 victory for Persepolis.
“I am very happy with result but we have not done yet. For us, the next match is always the most important match,” Persepolis coach Branko Ivankovic said in the post-match news conference.
“Paykan are a difficult team to beat and I am satisfied with the way we played against them,” the Croat added.
Persepolis lead the table with 46 points, 12 points clear of second-placed Foolad.