Iraq, who were almost kicked out of the competition two weeks ago after a dispute between their government and world governing body FIFA, registered their first win of the campaign when Rida scored from a free kick in the 28th minute.
The result lifted Iraq into third place in the group standings with four points from four games.
Australia and Qatar both have seven while China have three. The top two advance to the next stage of qualifying.
The defeat was the Socceroos first in the group and coach Pim Verbeek paid credit to the Iraqis for ending his side's unbeaten record.
"First of all I would like to congratulate Iraq for their good performance and victory tonight," said the Dutchman.
"Iraq are always a tough team and they have good players who put on a good performance."
Verbeek was not too despondent though with the result.
"We went into the game with an aim to get a draw and we put in a good performance today.
"We did our best to score and we created several chances but we were unlucky.
"Despite the defeat, we are still in a good position and we will go to Qatar for our next match aiming to get a win.
"The good thing about today's game is that we are getting accustomed to the weather in this region before our next match."