All five of the game's tries came in the first half at the Aviva.
Ireland ran into a 17-0 lead, thanks to a fine try from Simon Zebo and an intercept effort from Tommy Bowe.
However, Australia showed their class, scoring three tries in succession, with two of them coming from Nick Phipps.
A penalty from Jonathan Sexton left it at 20-20 at half-time.
There were just 9 points shared out by the two sides in the second half, but crucially it was Ireland who scored another two penalties and they held on to complete their third win this Autumn, after victories over South Africa and Georgia.
