After a 3-0 loss in their opener against a superior Korea Republic, the Joeys needed to avoid defeat to hold any realistic hopes of winning the tournament.
To add extra pressure, their FIFA U-17 World Cup fate also hangs in the balance, as a top-four finish at these AFC Championships is required.
Iraq were reduced to 10 men when Ali Kadhim was shown a red card in the 41st minute, but the sides were locked scoreless at half time.
Australia's Luke Duzel broke the deadlock in the 67th minute and Noah Botic doubled that lead less than five minutes later.
Iraq's Qasim pulled one back from the penalty spot, but the Joeys held on for a priceless three points.
Trevor Morgan's charges face Afghanistan in their final group match this Friday.
