In the match, held in Tehran’s Shahr-e Qods Stadium, Arash Rezavand opened the scoring for Saipa through a penalty in the eighth minute before Arman Ramezani doubled the tally in the 24th minute.
Ali Daei’s side sealed the win with two more goals in the final 20 minutes of the match.
Minerva’s hopes of making a comeback were dashed when Samuel Sarfo made it 3-0 with his effort in the 73rd minute, before Rezavand scored his second of the night eight minutes later.
Next Tuesday, Saipa will travel to Doha, Qatar to play Al Rayyan in the playoffs.