Bin Sultan grabbed the only goal of the game in the 57th minute, producing a neat finish after being set up in the area.
Al Shabab started brightly and Camacho delivered a dangerous cross into the six-yard box after five minutes but goalkeeper Mohammad Bagher Sadeghi reacted quickly to collect the ball.
A minute later Zob Ahan responded through Hossein Mahini, who dribbled into the penalty box from the right before sending in a dangerous cross which was cleared by keeper Waleed Abdullah.
Ahmad Mohamadpour missed a good chance for Zob Ahan in the 12th minute, shooting straight at the goalkeeper when well placed.
Zob Ahan then threatened again in the 24th minute through Esmail Farhadi.
He was put through from midfield with just the goalkeeper to beat but saw his effort well saved by Abdullah.
Less than a minute later, Farhadi came close to making amends for his miss but his shot from outside the area was well saved by Abdullah.
Al Shabab hit back and came close to breaking the deadlock on 29 minutes when Nada Mesad's dangerous cross into the area just needed a slight touch from one of his team-mates to find the net.
Brazilian striker Igor Castro then found the side-netting from the edge of the area in the 31st minute before Jalal Rafkhaei's right-footed strike flew wide 10 minutes before the break.
Al Shabab finally made the breakthrough in the 57th minute when Bin Sultan benefited from good approach play by his team-mates, collecting a pass with his back to goal before turning and firing into the net.
The advantage could have been doubled on the hour mark but Camacho’s close-range strike was blocked by a Zob Ahan defender.
Zob Ahan pressed forward in an attempt to find the equaliser and Rafkhaei delivered another dangerous ball into the area, but Abdullah was in the right place to deny Castro.
Substitute Mahdi Rajabzadeh wasted his side's last chance in stoppage time as he fired high over the bar from outside the area.