In the first half, the only goal of the match came between Australia and Tunisia.
Mitchell Dukes finished off a pattern attack with a delicious header.
The origin of the goal is, however, debated.
Referee Daniel Sieberts happened to foul Tunisia's Ellyes Skhiri in the counterattack before the goal.
- If this had happened to Sweden, we would have been mad, it would have been madness.
This goal would not have been approved, says expert Jonas Eriksson.
The victory is Australia's third in World Cup history.
It means that you still have the chance to advance in the group, which also includes France and Denmark.