Australia coach Guus Hiddink claimed "justice had been done" after his side scored three late goals to beat Japan 3-1 in Kaiserslautern.
Hiddink was unhappy with Japan's goal, scored by Shunsuke Nakamura after Atsushi Yanagisawa had collided with Australia keeper Mark Schwarzer.
"In the end justice was done in this game," Hiddink said.
"I think the referee will thank God for the result - it was a clear foul on the goalie."
Dutchman Hiddink was delighted with the resilience shown by his players.
"This team is nice to work with because they never give up," he said.
Everton midfielder Tim Cahill, who inspired Australia's victory by scoring their first two goals, said the win was a "dream come true".
"Just being a part of this World Cup means everything to all of us," he said.
"To get the goals is the icing on the cake. We look to moments like these from when we were kids dreaming of this situation.
"I'm just really happy to be part of it."