Hicham Aboucherouane had given Al Ittihad the lead with 80 minutes gone in the Group C clash at the Azadi Stadium before Alizadeh intervened two minutes from time to claim his side's third point in the competition.
Al Ittihad had the first chance of the game after 12 minutes when Brazilian midfielder Renato struck a powerful free-kick from distance but the ball rose over the crossbar.
Esteghlal threatened two minutes later when Hadi Shakouri's cross from the right was headed goalwards by Siavash Akbarpour but Al Ittihad goalkeeper Mabrouk Zaid tipped the ball over the bar.
The visitors began to dominate and they had a good opportunity to open the scoring after 28 minutes but Redha Takar headed Manaf Aboshgair's free-kick wide of the post as the first period ended goalless.
Esteghlal were the better side early in the second-half and spurned a good chance after 50 minutes when Hashem Beikzadeh's cross from the left was headed over by Ebrahim Taghipour.
The home side continued to press and went close again three minutes later when Beikzadeh produced another fine delivery that Akbarpour connected with from close range but Zaid made a point-blank save.
Esteghlal threatened from the resulting corner as Pirooz Ghorbani struck a powerful volley but Zaid was again in the right place to make the save.
The hosts were enjoying plenty of success down the flanks and fashioned another chance after 57 minutes when Farhad Majidi crossed but Arash Borhani fired over the crossbar.
Al Ittihad then took the lead against the run of play when Moroccan striker Aboucherouane unleashed a powerful left-foot drive that found the back of the nt just two minutes after the substitute had come on.
Esteghlal pressed for an equaliser and came close in the 86th minute as substitute Alizadeh got on the end of Beikzadeh's cross but his strong effort was well stopped by Zaid.
However, Alizadeh was not to be denied and two minutes later he headed home Fabio Januario's corner to ensure Esteghlal at least enjoyed a share of the spoils against the Group C leaders.
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