Australia 17-16 Ireland
World champions Australia held off a brave fightback by Ireland to earn a quarter-final clash with Scotland.
In an energy-sapping clash in Melbourne, the Wallabies led 14-6 at one stage only to be pegged back by a resilient Irish side.
Ireland put the host nation under some intense pressure in the second half but could not find the score that would have taken them in front for the first time in the match.
Defeat for Eddie O'Sullivan's men means they face in-form France in the last eight.
Australia got their first points of the match after 10 minutes when George Gregan slotted a drop goal.
The home side soon extended their lead when flanker George Smith dived over in the left corner three minutes later after the Irish defence had been stretched across the pitch.
Ronan O'Gara reduced the deficit with a penalty after Australia had been caught offside only for an Elton Flatley penalty to open up an eight-point advantage again for the Wallabies.
O'Gara and Flatley both missed penalties before O'Gara landed his second successful kick to make it 11-6.
Right on half-time, tempers boiled over when Shane Horgan caught Mat Rogers on the head with a boot.
The trouble quickly died down, but referee Paddy O'Brien, after consultation with his touch judge, sent both Rogers and Horgan to the sin bin.
Flatley and O'Gara continued to be wayward with their place kicks after the break, though the Aussie centre did extend his side's lead with another three-pointer.
But the tide was beginning to turn in Ireland's favour.
And they managed to breach the Australia defence on 50 minutes with a superb try from Brian O'Driscoll.
The video referee was brought in to judge whether the Irish ace had touched the ball down in the left corner before his feet went into touch, but the Irish faithful inside the stadium were never in any doubt.
With O'Gara landing the conversion, Ireland were within a point of the world champions.
Flatley kicked another penalty to make the gap four points, but an O'Driscoll drop goal with 13 minutes kept Ireland in the hunt.
The Irish continued to press, but Australia held on for victory - and a quarter-final against Scotland.
Australia: M Rogers; W Sailor, M Burke, E Flatley, J Roff; S Larkham, G Gregan (capt); B Young, B Cannon, B Darwin; D Giffin, N Sharpe; G Smith, P Waugh, D Lyons
Replacements: J Paul, A Baxter, D Vickerman, M Cockain, C Whitaker, M Giteau, L Tuqiri.
Ireland: G Dempsey; S Horgan, B O'Driscoll, K Maggs, D Hickie; R O'Gara, P Stringer; R Corrigan, K Wood (capt), J Hayes, M O'Kelly, P O'Connell, S Easterby, K Gleeson, A Foley
Replacements: S Byrne, M Horan, D O'Callagham, E Miller, G Easterby, D Humphreys, J Kelly.