Al Sadd qualified for the semi-final on a 5-3 aggregate win.
Al Sadd broke the deadlock through Akram Afif in the 27th minute. The youngster picked up Baghdad Bounedjah's lay-off in the box before lashing in an unstoppable shot past Rahmati to give his side a 4-1 aggregate lead.
Esteghlal's reply arrived in the 32nd minute when it equalized with the help of some good fortune. Rouhollah Bagheri's strike was fumbled by Meshaal Aissa and the ball fell into the net, levelling the score on the night.
As the second half kicked off, Esteghlal went on the attack with added vigor and was rewarded four minutes in, when Morteza Tabrizi rose highest to head in Farshid Esmaeili's delivery to put the visitor 2-1 ahead.
Needing just a goal to level the aggregate score, Esteghlal was rising in confidence but it was struck with a blow in the 50th minute when Rouzbeh Cheshmi was sent off for a second bookable offence.
Al Sadd managed to hold its own against their 10-man opponent for the remainder of the game, before being gifted a penalty deep into added time after Rahmati brought down Afif inside the box.
Tournament top scorer Bounedjah stepped up to score his 12th goal of the campaign to confirm his side's progression into the semi-final.
Al Sadd now face two more encounters against Persepolis in the semi-final, having played the Iranian side in the group stage.