Tries from wingers Reece Hodge and Marika Koroibete as well as a 12th of the season from fullback Israel Folau had given the home side a 20-13 lead with 15 minutes of the match remaining.
Waisake Naholo had crossed in the first half for the world champions and his fellow winger Rieko Ioane got their second in the 71st minute but Damian McKenzie missed the conversion and a 55-metre Hodge penalty gave the Wallabies a famous victory.
New Zealand beat Australia 54-34 in Sydney and 35-29 in Dunedin during the Rugby Championship and so were already assured of retaining the Bledisloe Cup for a 15th successive season.
Australia captain Michael Hooper was delighted with his side’s performance at full-time.
“Overwhelming sense of satisfaction,” Australia captain Michael Hooper said.
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“We didn’t win any comps tonight but it goes a long way to building confidence in this team.”
New Zealand were without World Rugby Players of the Year Beauden Barrett and Brodie Retallick but that didn’t stop them making a strong start.
The visitors had the better of the early exchanges and were pressing for the opening score when Hodge snatched Lima Sopoaga’s pass out of the air and raced 80 metres for a Wallabies try in the seventh minute.
The All Blacks were soon back on level terms, however, after going through 10 phases on the Australian line and making room for Naholo to cross untouched on the right wing.
Two penalties from Sopoaga put New Zealand 13-7 ahead before Wallabies star Folau cut between Naholo and flanker Liam Squire to score.
Bernard Foley missed the conversion and a penalty at the start of the second half and it was not until the 57th minute that the home side went ahead on the back of their third try.
A penalty kicked to touch was followed by a catch-and-drive and, with the referee’s hand raised to indicate another All Blacks transgression, Australia moved the ball wide for Koroibete to touch down in the corner.
The All Blacks were never going to fold and a Sonny Bill Williams offload made space for Ioane to race down the touchline for the score that set up the late drama.
New Zealand beat Australia 54-34 in Sydney and 35-29 in Dunedin in the first two tests and so were already assured of retaining the Bledisloe Cup for a 15th successive season.