The win over Tunisia keeps alive Australia's hopes of making the World Cup last 16.
Knowing defeat would mean an early exit from the competition, Graham Arnold's side came out of the blocks with gusto.
Mitchell Duke was the one who took advantage of the positive start, flicking Craig Goodwin's cross into the far corner to give them the lead after 23 minutes.
A small group of Australia fans behind the goal erupted in joy, which temporarily silenced the hostile and steadfast support for Tunisia.
Australia held their nerve to claim their first victory at a World Cup since 2010 after being jeered and booed throughout.
They survived a desperate onslaught from Tunisia in the second half, with Mathew Ryan having to make a save at his near post after Youssef Msakni forced him into a stop.
Harry Souttar made a number of key blocks and tackles as Australia dug in.
Australia, who lost to France in their first match, will take on a tough opponent in the second match, but with qualification in their own hands.
This was a crucial match for both nations as they face off against each other in order to progress from Group D.
Australia dominated the first 15 minutes of the game and Tunisia couldn't get out of their half.
The ease with which Australia were getting joy down that side will cause concern for Tunisia.
Duke ran over to the touchline to get a pat on the head from his team-mates after he scored one of those crosses.
The majority of Tunisia fans in the Al Janoub Stadium were silenced by that goal, but their side ended the first half with two big chances to equalise.
Just minutes before Tunisia captain Msakni tried to score, Australia centre-back Souttar made a crucial, sliding block to deny him.
Australia was put under a lot of pressure by Tunisia in the second half. Souttar stopped a dangerous counter- attack after another vital block by Mooy.
There was a lot of anxiety in the stadium when Tunisia's substitute was close to scoring a goal.
Australia went into their final group match with all to play for after holding on for a significant victory.
Tunisia takes on France in their last match.
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