The Irish stormed to the summit of Pool C by winning the group's pivotal match against the Tri-Nations champions and tournament second favourites at Eden Park.
Jonathan Sexton kicked two penalties and a drop goal while Ronan O'Gara weighed in with six points in Ireland's finest World Cup display.
They owed everything to the heroics of their pack, who battered Australia from start to finish.
Ireland possessed the two dominant forwards on the pitch in Paul O'Connell, who was outstanding once again, and the unstoppable Stephen Ferris.
Sean O'Brien became increasingly influential as the match unfolded, while tighthead Mike Ross led the rout of the Wallaby scrum.
Ireland refused to take their foot off the throat of their opponents' feeble set-piece, driving them into the turf time and again.
The Wallaby backs were more dangerous, but the Irish played smart rugby by choking the game up front to deny them possession.
Australia's day started badly when their highly influential openside David Pocock was ruled out of the match with a back injury.
The late withdrawal of hooker Stephen Moore also disrupted preparations and from kick-off they knew they were in for a challenging encounter.
Roared on by their strong travelling support, Ireland made a fiery start with O'Brien mixing it with the Australian forwards as the packs squared off.
The Wallabies began to make inroads around the breakdown, with a robust tackle from O'Brien stopping Will Genia in the nick of time.
O'Connor was more successful with a second shot at goal after Ireland's scrum had collapsed five metres out, the only time they were troubled at the set-piece.
The disappointment of Sexton sending a penalty wide was soon forgotten as Rory Best produced a cute offload to O'Driscoll, who burst into space.
Ireland's captain was soon brought down but his side had won a penalty and this time Sexton was on target.
The score sparked a superb spell from Ireland with O'Connell, Rob Kearney and Keith Earls making inroads before Sexton landed a drop goal to nudge his side 6-3 ahead.
Two successive penalties were conceded at the breakdown but O'Connor, who was taking an eternity to complete his kicks, was off target.
The pauses in between action were lengthy in the third quarter, but when the ball was in play Ireland were enjoying the better moments.
A second missed penalty from Sexton did not help the cause, however, and nor did blundering referee Bryce Lawrence, who first got in Reddan's way as he tried to distribute the ball and then failed to penalise James Horwill for being offside.
Australia were under pressure and Stephen Ferris produced the moment of the half when he picked up Genia at the base of a scrum and carried him 10 metres with the Irish pack piling in behind him.
Australia's backs served Ireland with a timely reminder of their potency when Cooper, Beale and Adam Ashley-Cooper created an opening out of nothing down the left wing.
Ferris and O'Brien went on the rampage to put the Irish back on the front foot, however, as the match continued to be balanced on a knife edge.
The two backs rows were prominent once more as Ireland drove deep into Australia's half, winning a penalty which Sexton sent between the uprights.
Gordon D'Arcy limped off in the 49th minute, so on came Ronan O'Gara at fly-half with Sexton moving to inside centre.
The Wallabies' situation deteriorated when their scrum buckled once more, but Sexton's penalty cruelly hit the right upright and then bounced over the head of Brian O'Driscoll.
Quade Cooper almost wriggled free 10 metres out from the line but Australia were spending precious little time in Ireland's half.
It was becoming all too easy as Australia's scrum collapsed once more and O'Gara, who had taken over the kicking duties, made no mistake.
The Wallabies' weakness at the set piece was killing them and Ireland struck once more, O'Gara landing his second penalty.
Australia attempted one last throw of the dice but the livewire Genia was denied by a try-saving tackle from O'Brien.
Ireland had the final say, however, when Tommy Bowe intercepted and ran nearly the length of the pitch only to be caught just short of the line.
Lawrence called offside after Conor Murray had scampered over but the game was already over and the Irish were able to celebrate a famous victory.
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