In a match held at the Behnam Mohammadi Stadium, Esteghlal edged past Naft Masjed Soleyman 1-0 in front of about 7,000 spectators.
Rouhollah Bagheri scored the winner in the 96th minute after the game ended in a goalless draw in regular time.
Esteghlal will face Saipa in Tehran’s Azadi Stadium in Round of 16.
The Hazfi Cup is the Iranian football knockout cup competition, run by the Iranian Football Federation.
Esteghlal is the title-holder and most decorated team with seven titles.