Historically, the Wallabies have held the edge over Ireland but the men in green have posted a win and a draw in the sides' last four meetings.
There was the memorable 21-6 success at Lansdowne Road in November 2006, and a late converted try from captain Brian O'Driscoll sealed a 20-20 draw at Croke Park in November 2009.
In Brisbane last year, Declan Kidney's men opened up a 6-0 lead courtesy of Jonathan Sexton's right boot and were still ahead on the scoreboard as half-time approached - 15-11.
But Australia scored a well-taken try by Quade Cooper before the break and two Matt Giteau penalties in the second half wrapped up a 22-15 win for the hosts.
There have also been some close Rugby World Cup battles between the nations. Who could forget Ireland's agonising one-point quarter-final defeat at Lansdowne Road in 1991, or the resilient display in going down 17-16 to the Australians in Melbourne eight years ago?
32-6 winners over Italy yesterday, Robbie Deans' side will be expected to beat Ireland next Saturday and extend their advantage at the top of Pool C.
Speaking at the team hotel in Auckland, former centre Paul McNaughton, a man who knows what it is like to beat Australia in this part of the world, remains upbeat about Ireland's chances against the second-ranked side in the world.
"The guys have played against Australia before. They know them. There's a level of confidence and a strong belief that on our day, when we play well and all the engines and cylinders are running smoothly, we can beat Australia," said the team manager.
"We have the ability and the team to beat Australia. We have to play very well and better than we have done over the last four or five matches.
"Underdogs is not a position or a name we would go looking for but we are clearly the underdogs based on the respective records in the last three or four games. That doesn't really worry us."
That Irish side, captained by Fergus Slattery, created history with 27-12 and 9-3 Test victories over the Wallabies in Brisbane and Sydney respectively.
O'Driscoll and company are more than capable of securing a similar result next weekend, but McNaughton agrees that there will have be significant improvements made.
"We've all had a chance to reflect and watch the performance (against the USA) on video. We were disappointed, disappointed not to get the bonus point and execute a few more try opportunities that we had," he admitted.
"We're happy with the win. All weekend we saw the so-called lower ranked teams put it up to the higher ranked teams.
"Everybody going into the game knew we were going into a game and not a practice session. That's the way it turned out.
"We didn't get (the bonus point) and there was some poor handling associated with that. Nevertheless, we're happy to win and must move forward now."
Meanwhile, Australia will be without winger Digby Ioane for Saturday's clash. A try scorer in the bonus point win over Italy, he fractured his right thumb midway through the first half.
The injury will require surgery to repair but Ioane, who expects to return later in the tournament, will stay in New Zealand with the squad while he recovers.
Highlighting how quickly form can change at this level, McNaughton added: "We always seem to bring our best out when our backs are against the wall.
"It's only five or six weeks ago when Australia were beaten by Samoa and everyone was writing Australia off. And a couple of good wins and winning the Tri Nations has put them clearly up there as favourites."
Follow the Ireland team in New Zealand on www.twitter.com/irfurugby.