The holder 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 it on its 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 opponent Syria, against whom a draw will be enough to seal qualification to the last 16, while Palestine is 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.