The Wallabies now lead the Rugby Championship clash in Perth by 26-12 at half-time and Barrett's dismissal will make it very hard for Steven Hansen's men to mount a second half comeback.
Australia's failure to insert a clause similar to the one that deprived the Kiwis of the cricket World Cup now seems regrettable given they haven't beaten the All Blacks in Auckland since the Ronald Reagan administration.
All Blacks lock Scott Barrett has been charged with a risky tackle and is facing a possible ban which would rule him out of Saturday's deciding Bledisloe Cup Test against the Wallabies in Auckland. However, that would require South Africa losing to Argentina in Buenos Aires later on Saturday.
The Wallabies started on the front foot and Lealiifano kicked the first points of the match with a sixth-minute penalty, before the breakthrough try quickly followed.
The home side's try-scoring was kick-started by winger Reece Hodge as he benefited from the vision and handling of the returning James O'Connor.
First, Jack Goodhue had the vision to chip into the open space and despite a TMO review of the tussle between Michael Hopper and Kieran Read, Anton Lienert-Brown's grounding stood. The offence occurred at a ruck just before half-time.
"But the All Blacks don't really do terminal decline ... there is no particularly daunting or unachievable task on it and a record loss one week can easily be a record win the next".
Opinion was split about the red-card online, with some fans saying it was too harsh, but others applauding Garces for making a tough call.
It took six minutes for their work to be rewarded, as New Zealand showed considerable fortitude in defence, but eventually a bullet pass out from White found Rory Arnold.
He was red-carded by French referee Jerome Garces for an apparent shoulder charge which struck Wallabies skipper Michael Hooper in the back and neck as the All Blacks were desperately defending their line.
That's the difference one great performance against the reigning world champions - admittedly reduced to 14-men in the second half - makes after the long spell of Wallabies' muddling and mediocrity.
The 24-year-old limped off midway through the first half in the All Blacks' 47-26 loss last night.
All Blacks head coach Steve Hansen blasted his team's poor discipline on Saturday after they crashed to defeat against Australia, but refused to be drawn on whether he thought Scott Barrett's red card was justified.