Australia, who were beaten 4–1 by France, won a World Cup match for only the third time in their history at the Al Janab Stadium.
Striker Mitch Duke scored the only goal of a tight game in the first half with a clever header as Australia desperately tried to silence the vocal Tunisia fans.
The Socceroos are second in Group D with three points from two games, with one game against Denmark.
“As a striker you need that confidence and belief that you can score in every match,” said the 31-year-old Japan-based centre-forward Duke.
“I was actually texting my family saying I’m going to score today.”