Duke's stellar header in Saturday's clash in Qatar raises Australian hopes of advancing to the knockout phase for only the second time.
The Socceroos, after losing 4-1 to France in their opener, bank three precious points after Duke's 23rd-minute goal against the Tunisians.
Another positive result against Denmark and the Australians could follow the feat of the fabled 2006 golden generation in progressing out of the group stage.
"(I'm) just hugely proud of the boys," delighted coach Graham Arnold said.
"They showed that great fighting Aussie spirit tonight. We were in their faces all the time. I just expect they made the nation very proud.
"The effort level was incredible. Again, when the doubters hate us, bring it."
The victory over Tunisia was Australia's first in a dozen years, since downing Serbia in 2010. The Socceroos also beat Japan in 2006.
And the oft-maligned Duke became just the eighth Socceroo to score at the World Cup.
His goal came from a sizzling move, with Australia pinging the ball from goalkeeper Mat Ryan into the net in just 15 seconds.
Ryan short-passed to the influential Harry Souttar, whose laser-like delivery triggered the attack.
From inside his own box, Souttar found Duke just inside the halfway line and, with a canny flick, the forward played in Riley McGree.
McGree fed Craig Goodwin, charging along the left flank, and the Adelaide United man whacked a low ball which deflected off Tunisian defender Mohamed Drager, one bounce, and skimmed towards Duke.
The Socceroos striker belied the degree of difficulty to angle a glancing header into the net.
"No words. When the ball hit the net, It's the best moment of my life and my football career," goalscorer Duke said after the game.
"I'm going to start crying because it's such a big moment.
"It's the best feeling in the world but I'm trying not to get too caught up with it because the job's not done yet, we've got one more game to win to get out the group."
"Honestly, I will go to war with these boys."
Tunisia, who had not conceded a goal to anyone bar Brazil in their previous 10 matches, gave Australia several anxious moments but a string of timely interceptions, not least from the magnificent Souttar kept them at bay.
The Tunisians ramped up the pressure in the second half - though the Socceroos almost sealed the deal in the 71st minute when Mathew Leckie, sliding towards a near-empty net, narrowly failed to connect with a low Jamie Maclaren cross.
But the Tunisians failed to break the Australian defence and remain on one point from their draw against Denmark in their opening game.
The Danes (one point) meet France (three points) at 3am AEDT on Sunday.
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