The holders suffered a shock 1-0 defeat five days previously but quickfire goals from Jamie Maclaren - his first for his country - and Awer Mabil in the opening period set them on their way at Rashid Stadium before Apostolos Giannou rounded off the scoring late on.
The first two goals arrived in the 18th and 20th minutes, Maclaren heading home Tom Rogic's cross before Mabil ghosted in to get on the end of Chris Ikonomidis' angled ball from the left flank - the winger picking up a second assist for Giannou at the end of regulation time.
Victory lifts the Socceroos to second in the Group B table, two points clear of their final opponents Syria, against whom a draw will be enough to seal qualification to the last 16, while Palestine are bottom on one point but are far from out of the knockout picture.
Graham Arnold had called on his players to come out fighting after that loss to Jordan and he must have been thrilled to see a two-goal lead opened up inside the first quarter of the game.
Rogic, playing with a broken hand suffered last time out, sent in an excellent cross from the right that was glanced home by Maclaren for the first.
And the advantage was doubled shortly afterwards as Mabil was left completely unmarked to steal in at the back post and convert Ikonomidis' delivery from five yards.
Australia ought to have put the game to bed shortly before the break when the two goalscorers combined, only for Mabil to blaze over at close range.
The Socceroos almost claimed a fortuitous third when Rhyan Grant's low cross deflected off Abdallah Jaber and struck the bar but the win was complete in the 90th minute as substitute Giannou rose unchallenged to head in another Ikonomidis centre as Arnold's men delivered the requisite response.
What does it mean? Socceroos bounce back impressively
No reigning champion has ever lost both of their first two games at the Asian Cup, and Arnold's side never looked likely to make unwanted history here, any fears settled by that early double strike.
Maclaren off the mark
Having made his debut in 2016, Hibernian striker Maclaren netted his first Socceroos goal thanks to a deft header. Rogic's left-wing cross had plenty of pace on it and Maclaren, with his back to goal, helped it on its way into the far corner beyond Rami Hamada.
Shot-shy Palestine lack creative edge
Noureddine Ould Ali's men did not muster a single effort on target in their opening 0-0 draw with Syria, and it was the same story here. They will have to find some attacking inspiration against Jordan in four days' time.
The teams conclude their group-stage campaigns on Tuesday, when Australia will look to secure their passage against Syria. Meanwhile, Palestine face already-qualified Jordan and still harbour realistic hopes of progression.