Noah Botic and Caleb Watts midway through the second stanza as the Joey were forced to claw their way back from 2-0 down for the second straight game.
The result keeps Australia with a shot of making it out of the group stage as one of the best third placed teams.
A clash against an undefeated Nigeria on Saturday morning will decide their fate with nothing less than a draw enough to secure their progression.
Early nerves once again had the better of the Trevor Morgan coached side as Hungary broke the deadlock only 14 minutes in through Peter Barath.
The Europeans doubled their lead five minutes later as Akos Zuigeber slotted home from the penalty spot after a little help from VAR.
The Joey's fought back and were unlucky to have not opened their account before the interval with two goals denied for offside and another effort controversially ruled to have not crossed the goal line.
Australia had all the momentum after the break despite trailing on the scoreboard.
It took until the 69th minute for the Joeys to finally claim a breakthrough when Botic slammed home from the penatly spot.
Five minutes later the Aussies levelled the scores through Watts.
Victory was in sight and with the bulk of possession the Joeys threw everything forward.
However, it wasn't to be with a desperate Hungarian defence clinging on for a point.
Australia go into their final game against Nigeria in third place in Group B with one point.
Nigeria remain undefeated after defeating Hungary 4-2 on match day one followed by a 3-2 win against Ecuador.
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