Duke tormented the Tunisian defence throughout the game with his physicality and was rewarded in the opening half when his glancing header beat the keeper, helping Australia log their first win at the World Cup in 12 years.
The 31-year-old reeled away in celebration holding up his hands in the shape of the letter "J" for his son Jaxson as his team mates embraced him near the corner flag.
"I spoke to my son when I got selected for the World Cup. As a striker you need that belief and confidence you're going to score in every match," he told reporters.
"I told my son I was going to share it with him, the gesture is the letter J. It's a moment I'm going to treasure for the rest of my life.
"Obviously the moment I scored was pure ecstasy for me. I'd heard only seven Australians had scored at the World Cup and I told Arnie (coach Graham Arnold) I'd be the eighth - or ninth."
Victory moved Australia up to second in the standings on three points ahead of the other game between group toppers France and Denmark.
The Al Janoub Stadium was a sea of red Tunisian fans with a handful of Australian supporters in pockets around the arena, but the goal silenced the Africans who had been in full voice.
"It was a really hard fought match, Tunisia is very physical and we knew they'd be aggressive and their fans create a hostile environment," Duke added.
"They get very passionate in the game and we had to match that in the game and also beat it."
The striker plies his trade for Fagiano Okayama in the second-tier J2 League in Japan, often spending long periods away from his family, and Arnold praised his commitment to the cause.
"I've got a lot of faith in the kid. I always know when he walks over that white line, he will give more than 100% for the team, for the jersey and the nation," Arnold said.
