The Irish, who had been beaten 23-11 by the All Blacks in Wellington the previous weekend, were hoping to notch their first win since 1979 over the Aussies in Australia and they did everything other than win the game.
They took the lead in the first-half when Denis Leamy drove over from a close range line-out, but those two Giteau penalties proved the difference in the end.
Berrick Barnes opened the scoring with a try in the fifth minute, but Leamy's response, converted by Ronan O'Gara, edged the Irish ahead.
The lead didn't last long before lock James Horwill profited from a delightful pass out of a tackle by Giteau for a try which the outside half converted. Giteau added a penalty to make it 15-7 at the break.
Giteau's second penalty three minutes into the second half gave the Irish a mountain to climb, but they re-grouped and gave the Wallabies a real rattle.
A brilliant piece of individual skill from Brian O'Driscoll, plucking the ball out of the air over his shoulder before charging 40 metres, should have led to a try, but the Irish skipper's inside pass to Paddy Wallace didn't hit the mark.
O'Driscoll made amends after 62 minutes when he finished off a great raid up the left touchline started by man of the match Rob Kearney and carried on by Tommy Bowe.
Ireland pressed for the winning score, but found the home defence in no mood to concede. The Irish finished off with an attack over 18 phases, but a knock-on ended their hopes.