Australia won a World Cup game for only the third time in their history with a dogged 1-0 victory over Tunisia on Saturday to revive their last-16 hopes.

Striker Mitch Duke scored the only goal of a tight game with a clever header in the first half and Australia then desperately held on to silence Tunisia's vociferous fans.

The Socceroos face Denmark -- who play France later Saturday -- in their final group game and the knockout round is in sight.

Their best World Cup performance came in 2006 when they also reached the last 16, in the days of Tim Cahill, Harry Kewell and Mark Viduka.

Australia had only ever won two matches at the World Cup before this and squeezed into this edition via a playoff.

But they started the better against a Tunisia team who held Denmark 0-0 in their opener and are looking to reach the knockout stage for the first time.

In the 23rd minute Australia took the lead their possession deserved.