Last weekend, Australia claimed a 27-19 victory over New Zealand in Sydney, but the Kiwis would pose different opposition on their home turf having not lost in front of their own fans in 33 matches.
Australia were matching their rivals blow for blow but on 22 minutes, New Zealand went over for the first try of the night after Carter provided Dane Coles with the ball, who proceeded to run half the length of the pitch before touching down, leaving Carter to add the conversion.
A penalty apiece saw New Zealand hold a 13-6 advantage at the break, but within the space of seven second-half minutes, they had extended their lead to 21 points.
After a penalty try also resulted in Cooper being sin-binned, Ma'a Nonu completed a well-worked move involving Coles and Ben Smith before Carter was given the opportunity to touch down in the corner as Australia were blown apart.
With 14 minutes remaining, Nonu recorded his second try after good work from Carter, before skipper Richie McCaw was given the honour of a standing ovation as he departed the pitch following what is likely to be his final appearance in front of his team's home fans.
Israel Folau ran over a consolation try for the Wallabies but it was far too little too late as New Zealand comfortably ensured that they retained the Bledisloe Cup.