Kurtley Beale sealed a night to remember for the Wallabies in front of over 61,000 at Optus Stadium in Perth.
Scoring 7 tries on the night, Australia dominated an always-dangerous New Zealand team, with the match turning a minute before half-time when the All Blacks' Scott Barrett received a red card for a dangerous shoulder-charge to Michael Hooper's head.
With only 2 games in this year's Bledisloe Cup series, a win or a draw next week at Eden Park will be enough to regain the trophy that has not been in Australian hands since 2002.
The match started explosively - despite scoring first with a penalty and then Reece Hodge running 20 metres to score after great work from James O'Conner, the All Blacks struck back with 2 quick tries.
But accurate kicking from Leali'ifano kept up the scoreboard pressure and the Wallabies went into half-time 16-12 ahead and crucially with a man advantage.
The 2nd half continued the high tempo for Australia with Rory Arnold driving over and Nic White with a superman dive to finish off a Samu Kerevi steamroller of a run, to put the Wallabies 26-12 ahead.
This only seemed to make the All Blacks more determined, ramping up the pressure and sapping the energy of the Wallabies, Beauden Barrett finishing off the attack sidestepping past 4 defenders to score the best individual move of the match.
But tries 7 and 8 of the night finally broke the resistance of the reigning Bledisloe Cup holders - Koroibete and Hodge with his 2nd of the night.
Laumape kept it close for New Zealand scoring straight from the restart to make it 40-26 but Beale deservedly finished the try-scoring on a memorable night in Western Australia.
Rugby - All Blacks v Wallabies - LIVE on 10 Bold and streamed LIVE on 10 play. Broadcast commences - 5.00pm AEST Saturday 17 August.