Jonathan Sexton and Ronan O'Gara each landed two penalty goals and Sexton added a drop goal to inflict the Wallabies' first pool-stage loss at a World Cup since they went down to host South Africa in 1995.
James O'Connor kicked two first-half penalties for Australia, which conceded five scrum penalties and struggled to display any fluidity after having lost flanker David Pocock and hooker Stephen Moore to injury or illness in the hours leading up the match at Eden Park.
Ireland can almost certainly avoid defending champion South Africa and the top-ranked All Blacks on its side of the knockout draw by beating Italy on Oct. 2. That fate is now likely to befall the Wallabies, who are ranked six places higher than Ireland at No. 2 by the IRB.
After some heartbreaking World Cup defeats to the Australians, including the 1991 quarterfinal in Dublin which has become part of the tournament's folklore, the Irish were euphoric.
"It was the performance we knew we had in us. We had incredible support and it was our job to give them something to shout about, and thankfully we managed to do that," Ireland captain Brian O'Driscoll said. "We had to go to the well today, we had to dig deeper than we had done. And thankfully we managed to do that."
The Irish ran back onto the field after the match to salute the thousands of travelling fans but O'Driscoll later reminded them that only half the job was done in the group stage.
"Let's not lose sight of the fact we have two more games," he said.
Australia has the youngest squad at the tournament, but came into the competition full of confidence after beating defending World Cup champion South Africa and No. 1-ranked New Zealand last month to claim its first Tri-Nations title in a decade.
That will certainly be deflated now. The Irish pack bullied the Australians into submission in the setpiece, with prop Cian Healy reveling so much in the wet and slippery engagements he was adjudged player of the match.
And the more the freewheeling Wallabies backs tried to counter with running rugby, the more it backfired.
"The Irish did well to spoil our ball. We couldn't get any momentum," Wallabies captain James Horwill said. "We played some dumb footy.
"We were giving away silly penalties. We didn't do well to hold on to the ball enough."
Coming off an unconvincing 22-10 win over the United States after four straight losses in warmup matches, Ireland had been written off by the critics. But Australia had no answer to a committed and dynamic performance from the Irish forwards and often fell foul of referee Bryce Lawrence.
The Wallabies had wobbled in the first half of their 32-6 win over Italy last week, being held to a 6-6 scoreline at halftime before scoring four second-half tries. And that initial disjointed and erratic form returned on Saturday with few players enhancing their reputations.
The Wallabies' double blow to their starting lineup didn't help, losing Pocock because of a back injury before Moore withdrew in the hours leading up to kickoff due to illness.
Ben McCalman made his first test start on the openside flank to take over from Pocock, and Tatafu Polota-Nau made only his fifth start in 26 tests in replacing Moore.
"Ireland were very effective in denying us momentum," Australia coach Robbie Deans said. "The nature of the game at World Cups is the passion of the defence and you can't be sure of getting any momentum."
Ireland unsettled the Australians with some quirky plays and attacking defence which caught the Wallabies offguard.
It started with a quick tap from inside Ireland's quarter after receiving a penalty in the opening minutes, spreading the ball wide for winger Tommy Bowe to grubber ahead in an enterprising move.
Australia dominated territory in the opening quarter but trailed 6-3 on the scoreboard — flyhalf Sexton making the most of Ireland's brief early forays beyond halfway by landing a penalty and landing a well-taken dropped goal from the quarterline. O'Connor missed a shot at goal before landing a penalty.
Given more of the ball, the Irish lifted, but ruck infringements by backrowers Sean O'Brien and Jame Heaslip were hurting them, although O'Connor could only land one of two further kicks for a 6-6 scoreline.
Australia's scrum fell foul of Lawrence twice in the first half and was dominated by the Irish pack on one memorable occasion. With his scrum being wheeled, Australia scrumhalf Will Genia tried to quickly clear the ball but was picked up and carried backward by flanker Stephen Ferris.
The ebb and flow continued in the second half.
Quade Cooper launched one counterattack from deep, linking with Kurtley Beale before the final pass went astray. The Irish then hit back. O'Brien making a half break as play travelled to the other end of the pitch for another penalty goal from Sexton in the 50th for a 9-6 lead.
The Wallabies marched back into Ireland's quarter, Cooper scooted on the outside of Paul O'Connell but his flicked pass to an outside support only meters out from the line was blocked and the chance was gone.
Ireland led 12-6 when substitute Ronan O'Gara kicked penalties in the 63rd and 71st minutes from Australia's fourth and fifth scrum infringements.
In desperate late attacking raids, Australia hammered away with phase after phase but the Irish defence held firm and almost even scored a late try when Tommy Bowe streaked 90 metres before being cut down by O'Connor in a brilliant tackle.