Arnold expects plenty of hangovers in Australia after a moment of Mitch Duke magic delivered a 1-0 victory over Tunisia at the World Cup.

Duke's stellar header in Saturday's clash at Al Janoub Stadium in Qatar gifted his nation a third-ever triumph at the cup finals.

A win or draw against Denmark in four days' time and Arnold's motley mob of Australians from mainly second-tier leagues will match the feats of the fabled 2006 golden generation in progressing from the group.

But Arnold has ordered his players to temper their celebrations after Australia's third win from 18 games at World Cup finals.

"I just said to them, no doubt the nation is extremely proud, but we have done nothing," Arnold told reporters.

"You (players) have achieved something we can talk about after the tournament. But we're here to go as far as we can go.

"I don't want any celebration ... get ready for the next one."

Arnold had a different message for folks back home, though.

"Fans back at home, it's a moment they'll remember for the rest of their lives ... there will be a few hangovers in the morning," he said.

The Socceroos, after losing 4-1 to France in their opener, bank three precious points thanks to oft-maligned striker Duke.

In the 23rd minute, Duke met a skimming one-bounce cross and, with a glancing header that belied the degree of difficulty, became just the eighth Socceroo to score a World Cup.

"It's the best moment of my life," he said.

The victory was Australia's first at the finals since downing Serbia in 2010. They also beat Japan in 2006.

And the Socceroos kept a clean sheet at a cup for the first time since 1974, chiefly because of Harry Souttar.

In just his third senior game since recovering from a knee reconstruction, Souttar was simply superb with a string of interceptions and blocks.

"We were hanging on for a little bit towards the end ... but I am just so pleased," Souttar said.

"When the final whistle went, just the relief - all that hard work we have put in so far and over the qualification stages has come to that."

Aaron Mooy was magnificent in midfield, controlling play with precise passing and a supreme spirit.

"It's amazing," Mooy said. "Buzzing for everybody, that it makes them happy. That is the beauty of playing for the national team, especially at a World Cup."

Wingers Craig Goodwin and Mathew Leckie were also influential.

"Proud," Leckie said. "But we have got to go again in a few days. Nothing has been done."

Captain Mat Ryan, who made a string of late saves, echoed the theme.

"It's what dreams are made of," the goalkeeper said.

"It's a great feat, what we have done. But we're hungry for more."

Midfielder Jackson Irvine said following Arnold's edict and muting celebrations would be difficult.

"I have got to acknowledge what we did and what a big deal it was ... and how big that is for me and how much it means for everybody else," Irvine said.

"But I have got to let it simmer and let it fire us again in four days' time."

The Australians (three points) meet Denmark (one point) at 1800 local time on Wednesday (0200 AEDT Thursday).

Group leaders France (six points) are assured of progressing regardless of their result against Tunisia (one point).

Australian Associated Press