In the match, held at the Pandit Jawaharlal Nehru Stadium on Friday, Shahriyar Moghanlou opened the scoring for Persepolis in the 24th minute.
Isa Alekasir was brought down into the penalty area in the 23rd minute and Mehdi Torabi made the scoreboard 2-0 for Persepolis.
The lead was widened further two minutes into the restart as Moghanlou turned provider, sending a deep cross from the left flank to Alekasir, who charged into the box before coolly slotting home.
Persepolis added to FC Goa's misery when it made it 4-0 after Kamal Kamyabinia thumped his effort into the back of the net in the 58th minute after Ali Shojaei’s header off a corner was blocked by the home side’s defenders.
While Persepolis will look to confirm its Round of 16 spot against Al-Wahda on Monday, FC Goa will target the first win of its debut campaign when it plays Qatar's Al-Rayyan SC.