A first-half header from Mitch Duke was enough to see off Tunisia and ignite Australia's hopes of progressing to the World Cup knockout stages in a 1-0 victory.
Duke converted Craig Goodwin's left-wing cross in the 23rd minute with the Socceroos having to withstand some late pressure to secure a win that means they head into their final Group D clash with Denmark with all to play for.
Tunisia have a solitary point from their two games and will have to beat defending champions France on Wednesday and hope other results go their way.
Australia shaded a frantic opening but could not profit from a series of crosses into the Tunisia box.
Delivering the ball from wide areas was clearly a key part of the Australia strategy and it paid dividends midway through the first half. Duke started the move with a deft touch in midfield before racing into the box to cleverly glance Goodwin’s deflected cross past Tunisia goalkeeper Aymen Dahmen.
Tunisia grew as an attacking force as the first half progressed and could have levelled twice before the break.
After 41 minutes, robust play from Issam Jebali saw him pick out Mohamed Drager at the far post only for defender Harry Souttar to race across to block his goalbound shot.
The tireless Jebali then turned up on the right but his low centre was fired wide by captain Youssef Msakni.
Tunisia dominated possession in the second half but their desperation to find an equaliser almost saw them undone again after 71 minutes - substitute Jamie Maclaren escaping down the left before delivering a low cross that was inches in front of the sliding Mathew Leckie.
A second goal was not required in the end as Australia's resolute backline - in which Souttar was outstanding - did enough to keep Tunisia out and register just the Socceroos' second clean sheet in 18 World Cup matches.