Australia had retaliated from 18 points down to start to lead the pack through Nic White’s long-range 77th-minute penalty.
It appeared like the hosts had won when Lalakai Foketi secured a turnover penalty in front of his own goal posts.
However, referee Mathieu Raynal overturned his ruling for time-wasting to allow New Zealand a final chance to strike.
The home defence was drawn in by the visitors’ succession of forward rumbles, and when the ball was turned wide, Barrett had room to slide over and excite his teammates in Melbourne.
In response to a chorus of catcalls, Raynal left the field after awarding New Zealand a scrum after concluding that Australia fly-half Bernard Foley had taken too long to line up his kick to touch.
“Absolutely gutted,” said Australia captain James Slipper to Stan Sport.
“I don’t know what to say. We really wanted to put in a performance. That is probably the most gutting way to finish a game.”
Australia coach Dave Rennie said: “Of course the clock stopped, so there was no real urgency to do that.
“It lacks a little bit of feel for such an important moment in the game.”
The victory assures that New Zealand will keep the Bledisloe Cup for a 20th consecutive year and puts them clearly at the top of the Rugby Championship standings as they try to defend their southern hemisphere title.
When the teams meet in the last round on September 24 at Eden Park, Australia will attempt to get revenge.
