Kuwait led early against the run of play through Hussain Fadel at AAMI Park on Friday, but Ange Postecoglou's men fought back, led by young midfielder Massimo Luongo, who set up the home side's first goal and scored the second to give Australia a 2-1 lead at half-time.
A host nation had not won the opening game of an Asian Cup since 1968 when Iran, who went on to lift the trophy, defeated Hong Kong 2-0.
But Australia went for the kill from the opening minute of the second half and deservedly extended their advantage just after the hour mark when captain Mile Jedinak struck from the penalty spot. James Troisi added a fourth in stoppage time with a close-range finish.
The victory ended a three-game winless run for Australia and is just the third in the Postecoglou era.
After a tidy enough start from Postecoglou's side without properly threatening Kuwait's goal, the hosts were stunned in the eighth minute.
An unmarked Hussain sent a diving header past Mat Ryan from Kuwait's first corner thanks to sloppy defending by the home team.
The Australians - both those on the pitch and in the stands - looked shell-shocked, but, as the half wore on, their high pressing forced Kuwait further and further backwards, although any genuine creativity was lacking.
Luongo finally provided the moment of quality the home team needed in the 32nd minute, turning away from two markers after Ivan Franjic's throw-in and then cutting back to Tim Cahill, who made no mistake from near the penalty spot.
The goal seemed to inspire Luongo and his attacking midfield partner Troisi, as they began to threaten Kuwait's two deep banks of four.
Australia edged 2-1 ahead two minutes before the break, Franjic showing some skill to leave his opponent on the deck before swinging a cross to the near post where Luongo rose to nod the ball past Hameed Youssef.
Any fears that half-time would slow Australia down were dispelled almost immediately as they dominated the opening 15 minutes to eventually score a third.
Cahill forced a superb save out of Hameed in the 59th minute, before Mathew Leckie hit the crossbar, while the goal was the result of another fine attack down the right involving Luongo and Franjic before Robbie Kruse was felled in the box in the 61st minute.
Jedinak made no mistake with the penalty and, although Kuwait had some chances to score a second goal - none better than Fahad Al Ansari's drive that Ryan tipped onto the bar - Australia deservedly triumphed, eventually scoring a fourth when Troisi pounced in stoppage time.
Get the best features, fun and footballing frolics straight to your inbox every week.