Arash Rezavand was on target for Esteghlal with a header in the 25th minute. Nassaji defender Alireza Ebrahimi scored an own goal in the 34th minute.
Mohammad Mohebi made a brace in the 57th and 89th minutes.
Persepolis, who has recently won the Iran league title, will meet Havadar in the other semifinal match in Tehran on Thursday.
Esteghal is the most successful club with seven titles, followed by Persepolis who has won six times.