The All Blacks were 13 points down within 11 minutes but turned things around to deservedly earn their second victory from the past three Test matches in Sydney.
With both sides coming off defeats in South Africa, victory was vital.
But after the electric start in which Wallabies fly-half Matt Giteau scored all 13 points, Australia had to absorb sustained pressure from a much quicker All Blacks side.
Giteau, hooker Jeremy Paul and centre Morgan Turinui all suffered match-ending injuries in the first half as New Zealand took the game to the home side.
The Wallabies had seemed to be cruising early on with Giteau landing two penalties and a fine individual try which English referee Tony Spreadbury awarded after consulting the video referee.
The wheels then fell off, however, as New Zealand took control.
Daniel Carter landed a penalty before scrum-half Piri Weepu crossed the line for his first All Blacks try in only his third Test.
Carter landed the conversion to reduced the arrears to 13-10 at half-time.
The second period was totally dominated by the men in black.
Carter levelled the scores four minutes into the second half with his second penalty, and after that it was all New Zealand.
Quick thinking from flanker Richie McCaw gave New Zealand a deserved lead in the 56th minute.
McCaw, who was named man of the match, took a quick tap and bulldozed his way over the line from 10 metres.
Carter added the extra two points to give the visitors a 10-point buffer.
Winger Joe Rokocoko sealed the win nine minutes from time with the try of the match. Receiving a pass in his own half, he kicked ahead to touch down under the posts with the Wallabies defence in ruins.
Substitute Luke McAllister, who had replaced the injured Carter, added the conversion to seal the comeback.