In a game that was mostly devoid of any genuine chances, both sides were repeatedly let down by a lack of quality and invention in the final third.
The result means Zob Ahan now top Group D on four points, one ahead of Emirates after the latter overcame Al Rayyan 2-0 at home. Al Shabab, meanwhile, now have two points from their opening two games.
Last year's AFC Champions League finalists almost began in explosive fashion as Mohammmad Reza Khaletbari saw a spectacular overhead kick from the edge of the box whistle just past Waleed Abdullah's post as the keeper struggled to make up the ground with just two minutes on the clock
Ghasem Hadadifar then drew a fine save out of the Al Shabab keeper when his dipping strike was turned over by Abdullah at full stretch after quarter of an hour. Hossein Mahini then headed a diagonal ball delivered deep from the right flank just over the bar three minutes later as the Iranians made all the early running.
It took 27 minutes for Al Shabab to have their first shot on goal when Abdulaziz Saran fired well wide from a tight angle and the sides went in at the break level.
The second period followed much the same pattern as the first with Zob Ahan enjoying the better of what little attacking play there was.
Seyed Hosseini saw a neat back-header from a free-kick on the left narrowly clear the crossbar in the 63rd minute and two minutes later, Igor Castro spurned a good opening when he directed a powerful header from eight yards out down into the turf and Abdullah was able to claw the ball away.
Al Shabab substitute Alhassane Keita tested Shahab Gordan with a shot from range that the Zob Ahan keeper collected at the second attempt in the 80th minute before skipper Marcelo Taveres saw a powerful header flash the wrong side of the Zob Ahan keeper's near post with five minutes remaining as both sides settled for the draw.