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. Australia sit second in Group D with three points from two games, having been well-beaten 4-1 by holders France in their tournament-opener. 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. Graham Arnold's Australia don't have players of that ilk but they have lots of heart and kicked off to deafening whistles in front of 42,000 at Al Janoub Stadium, where their fans were heavily outnumbered. Each Australia touch was met with whistles from the throbbing ranks of Tunisia's bouncing, bellowing and flag-waving supporters. 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. The match was being shown on primetime Saturday night television in Australia and viewers saw their gritty side dominate the first 15 minutes, without mustering a shot. Tunisia had the first sniff of goal in the 19th minute but skipper Youssef Msakni was squeezed out, then defender Mohamed Drager blazed over. In the 23rd minute Australia took the lead their possession deserved. Craig Goodwin, who scored the opener in the loss to France, crossed from the left and the ball ricocheted for Duke to glance his header back over his own shoulder and into the net. The Japan-based centre-forward, 31, exchanged angry words with the Tunisian bench when he was bundled over on the half-hour mark. The skirmish ended in a shake of the hand with substitute Hannibal Mejbri, the Manchester United teenager. Another English-based player, defender Harry Souttar of Stoke City, made a heroic last-ditch block from the dangerous Msakni as half-time approached. Tunisia's fans had their heads in their hands in injury time when Msakni finally escaped Souttar, only to sidefoot wide from close range. Coach Jalel Kadri brought off Drager at the break and replaced him with a midfielder, Ferjani Sassi, and a match that had simmered up to that point threatened to boil over. Australia were playing on the break and were inches away from a second but Mathew Leckie could not connect on a low cross as he slid in front of goal. Minutes later goalkeeper and skipper Mathew Ryan denied Msakni from close range and Australia just about held on under intense pressure to leave Tunisia's World Cup campaign in deep trouble.