An early six-point goal by Aidan O'Shea helped Ireland lead 12-3 and they were 21-13 ahead after the first quarter.
A further O'Shea goal and successful Conor McManus penalty extended Ireland's lead to 43-23 at half-time.
However, Ireland lost their way in the final two quarters and a late Eddie Betts goal left the Irish hanging on.
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Joe Kernan's Irish side appeared to make the mistake of opting to go defensive in the second half of the game.
With the hitherto subdued Nick Riewoldt becoming a factor in the game, the Aussies began to finally play with fluency and the visitors will probably feel they should have won the game after squandering a number of goal opportunities.
In front of 38,386 spectators at GAA headquarters, Ireland make a fast start with O'Shea fly-kicking in his first goal to the roof of the net in the third minute after the Aussie defence had failed to deal with a diagonal ball from McManus.
The visitors's defence continued to be all at sea during the remainder of the first quarter with Diarmuid Connolly, McManus, O'Shea and captain Bernard Brogan (twice) knocking over three-point overs.
Australia did cut Ireland's advantage to 21-13 by the end of the first period but more sloppy defending gifted Mayo star O'Shea his second goal three minutes after the restart.
Ireland's third and final six-pointer came late in the second period as McManus coolly slotted a penalty after Donegal's Paddy McBrearty had been fouled before palming the ball to the net.
Leading 43-23 at the half-way point, Ireland appeared to change their tactics in the third quarter.
Whatever led to the change in the flow of game, Irish energy levels dropped and seven successive points from Riewoldt helped reduce the home team's advantage to 50-39 by the end of the third quarter.
As Ireland continued to run out of steam, they only managed to score five points in the final quartet but crucially, Betts's goal didn't come until three minutes from time.
The Aussie six-pointer cut Ireland lead to 55-49 and was quickly followed by another three points from Port Adelaide star Robbie Gray.
However, time then ran out for the visitors as Irish skipper Brogan kicked the final point of the game before lifting the Cormac McAnallen Trophy.
Ireland clinched a 56-52 victory in Saturday's International Rules Test at Croke Park as Australia's late brave fight-back came up just short.