Having fallen behind to Fernando Baiano's early opener, Hossein Kazemi equalised on the stroke of half-time for the Iranians after Hashem Beikzadeh hit the bar with a header.
Arash Borhani missed a second-half penalty, Khosro Heydari saw a volley smack the crossbar and substitute Ali Alizadeh missed an empty goal as Esteghlal dominated their UAE opponents and will be frustrated to only take a point from the Group C encounter.
Al Jazira had taken the lead after nine minutes. Rafael Sobis produced a bit of trickery on the left edge of the box but saw his fierce shot deflected behind.
The resulting corner was cleared as far as Marcio Rozario and his shot from 25 yards through a crowd of players was parried by keeper Vahid Talebloo into the path of Baiano, who hammered the ball into the roof of the net with the Esteghlal defence absolutely static.
Esteghlal looked to hit back quickly and when Al Jazira defender Salem Masoud was unable to head clear a long pass knocked towards Borhani, the striker found himself with the ball at his feet but keeper Ali Khaseif was quickly out to smother.
The visitors wasted a chance to double their lead on the half-hour mark when a neat one-two presented Ibrahim Diaky with a chance but his weak shot was kicked away by Talebloo.
Esteghlal came agonisingly close to an equaliser when Beikzadeh headed Heydari's free-kick against the bar and the ball was cleared.
Esteghlal were very much in the ascendancy as half-time approached and Heydari's driving run into the box and subsequent cross broke to Kazemi but he pulled his shot disappointingly wide.
But the midfielder made up for his miss moments later when he shinned home Siavash Akbarpour's corner from three yards out to draw the hosts level.
Akbarpour saw a volley from another Heydari cross excellently tipped over the bar by Khaseif just before the hour mark and Esteghlal were then handed a glorious opportunity to go in front in the 61st minute, which they wasted in bizarre circumstances.
Akbarpour latched onto Heydari's long ball but the forward was brought down in the box by Masoud and referee Ravshan Irmatov pointed to the spot.
Borhani stepped up to take the penalty but came to a complete stop just before striking the ball after seeming to slip before sidefooting weakly into the bottom left corner after a lengthy pause.
Al Jazira complained mightily and Irmatov ordered a re-take, presumably for unsporting conduct, and Borhani's second attempt was palmed away by Khaseif diving to his right.
Another fantastic chance went begging for Esteghlal with 13 minutes to go as Heydari saw a superb 25-yard-volley cannon back off the bar and substitute Alizadeh then embarrassingly headed over from six yards with goal at his mercy and Khaseif nowhere.
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