Hordes of Irish fans are expected to attend the pivotal clash in Pool C, which sees Brian O'Driscoll's side meet the World Cup's second favourites.
But Kiwis are also throwing their weight behind the green cause in the hope their fierce rivals will be humbled.
"Throughout our stay in New Zealand we've had a lot of support," Best said.
"For this game it's not just from the Irish, for whatever reason the New Zealanders will be supporting us as well. It's great.
"We want to play in big games and on the big stage and there's no bigger stage than the World Cup."
Australia's blindside flanker Rocky Elsom is well known to Irish rugby after a string of outstanding performances helped Leinster win the 2009 Heineken Cup.
The 28-year-old was relieved of the Australia captaincy during the Tri Nations, but having been restricted to just six games in 10 months due to injury, there is evidence he is almost back to his best.
"At Ulster we had a few bad experiences against him. He's obviously a quality player," Best added.
"The captaincy was an internal matter and you can read into that whatever you want.
"But the bottom line is that his name is on the team sheet tomorrow and we'll have to watch him.
"He's a very strong ball carrier and is very aggressive in defence.
"We know a little bit more about him than most in terms of his idiosyncrasies, but he's a world-class player with or without the captaincy.
"He looks like he's back to the form that brought Leinster the Heineken Cup."
Best denies the Wallabies scrum continues to be their Achilles heel, though he views Ireland's set-piece as a potential weapon.
"A lot has been made of their scrum, but during the Tri Nations they put the South Africa scrum to the sword," he said.
"Our own scrum has come a long way over the last 12-18 months. We feel like we're in quite a good place with it, we try to exert some pressure there."
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