Persepolis midfielder Ehsan Pahlavan opened the scoring for the host in the 10th minute but Mohammad Reza Azadi leveled the score 10 minutes later.
Referee Vahid Kazemi awarded a penalty to Persepolis in the dying moments of the first half and Mehdi Torabi converted his penalty.
Mohammad Alinejhad and Azadi scored two goals in the 53rd and 65th minutes, respectively and sealed an away 3-2 win for Aluminum.
Aluminum will play Khalij Fars Mahshahr in the semifinal round.
Esteghlal will also host Nassaji Monday night at the Azadi Stadium in the quarterfinal round.