Al Shabab recorded a 3-1 win in Qatar over Al Gharafa last week and Piroozi beat Sharjah of the United Arab Emirates by the same score but neither side was able to find the crucial breakthrough at the King Fahd International Stadium.
The result kept the two sides a point clear of Al Gharafa, who won 2-0 at Sharjah earlier in the evening.
Piroozi captain Karim Bagheri had a glorious chance to open the scoring early on but after the ball dropped for the unmarked midfielder on the penalty spot, he only managed to fire into the grateful arms of Al Shabab goalkeeper Waleed Abdullah despite having the goal at his mercy.
The home side enjoyed more of the possession but failed to create a clear chance as Abdullah Shuhail attempted to find the bottom corner from the edge of the area, only to see his curling right-footed effort drift the wrong side of the upright with Alireza Haghighi scrambling across his goal.
At the other end Alireza Vahedinikbakht rose highest to meet a corner, but Waleed was alert to make the low save.
Five minutes before the break the home side almost handed Piroozi the opener as Ali Karimi pounced on a loose back pass but after cutting into the area, he scuffed his shot and Naif Al Qadi recovered to block the effort.
Piroozi’s dominance of the later stages of the first half continued but they had only a wayward strike from Bagheri to show for it.
Nassir Alshamrani looked to hand the home side a perfect start to the second half as he showed a turn off pace to beat his man and provide a pin point cross to the front post from the byline, but Saleh Sadeeq was unable to direct his header on target.
After tempers briefly boiled over midway through a tightly contested second half, Karimi was denied an almost certain opener with 16 minutes remaining as Sadeeq produced a last ditch tackle to deny the influential midfielder after he had charged into the area unchallenged.
Substitute Hamidreza Asgari almost made an instant impact after replacing Karimi with 10 minutes remaining but after dancing around a lunging challenge on the edge of the area, his shot lacked power and failed to trouble Waleed.
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