DOHA, Qatar (AFP) — Goal hero Mitch Duke said he had a feeling he would score after his header gave dogged Australia a 1-0 World Cup win over Tunisia on Saturday to revive their last-16 hopes.

The striker’s clever looped header in Qatar put Australia in front in the 23rd minute and they desperately held on in the second half to silence Tunisia’s vociferous fans.

The Socceroos sit second in Group D with three points from two games, having been well-beaten 4-1 by holders France in their tournament opener.

They face Denmark — who play France later Saturday — in their final group game and the knockout round is in sight.

Australia’s best previous World Cup performance came in 2006 when they 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 play-off.

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 half.

Australia took the lead their possession deserved midway through the first half.

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.

Defender Harry Souttar of Stoke City then made a heroic last-ditch block from the dangerous Youssef Msakni as half-time approached.

Tunisia’s fans had their heads in their hands in injury time when Msakni finally escaped Souttar, only to side foot wide from close range.

Coach Jalel Kadri brought off defender Mohamed 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 late 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.

Tunisia’s World Cup campaign is in deep trouble and they face a daunting task in their final group game after taking just one point from two matches.

They must beat the defending champions France to have any hope of progressing.