The 2015 AFC Asian champions left Kuwait City with the points but also left the hosts ready to fire head coach Romeo Jozak.
Kuwait thrashed Nepal 7-0 last Thursday - in their 2022 World Cup Group B second round qualification opener - and approached the clash with Australia with some confidence.
The Socceroos, however, scored all three goals in the first half with a Mathew Leckie brace and a strike from Aaron Mooy doing the damage.
On Wednesday, the technical committee of the KFA, which oversees all national team activities, recommended that Jozak be fired.
It was suggested that the coach, formerly the technical director of the Croatian FA - who was also in the running to take the same role in Australian football in 2014 - be replaced as soon as possible.
With only the top team from each of the eight groups assured of a place in the next stage, along with the best four second-placed finishers, the pressure is on for all Asian nations.
As well as Kuwait, the Socceroos will face Jordan, Nepal and Taiwan in the group.
The home defeat was therefore a huge blow to Kuwait.
“We know that we are unlikely to challenge Australia for the first place in the group,” a high-ranking member of the KFA told The World Game.
“We were always challenging for second place but to lose three goals in the first half at home to Australia is not good enough. It means but we have to make sure that we collect 12 points against Nepal and Taiwan and even that may not be enough.”
There was criticism in the Middle East nation that against Australia star player Bader Al Mutawa was left on the bench for the first half.
By the time the veteran forward made an entrance, it was all too little, too late.
Jozak is a highly respected tactician but there was disquiet in the KFA at what was seen as overly conservative tactics especially in the first half.
Australia host Nepal in the next round of games on October 10, while Kuwait faces a tough trip to Jordan.
