Australia gave itself a huge boost ahead of the World Cup when it stunned a New Zealand side reduced to 14 men for half the match 47-26 in a thrilling Rugby Championship test on Saturday.
Lock Scott Barrett's dismissal for a dangerous tackle just before halftime undoubtedly had a big impact on the contest but the Wallabies were well worth their first win over the world champions since 2017.
Winger Reece Hodge scored two of their six tries as Australia ran up its highest tally of points in 165 tests against the All Blacks and gave itself a chance of regaining the Bledisloe Cup it last raised aloft in 2002.
Australia, which plays the second Bledisloe test in Auckland next week, could yet win the Rugby Championship for the first time since 2015 but the Wallabies will need Argentina to beat South Africa in Salta later on Saturday.
That will matter little to Michael Cheika and his team, which has endured four largely miserable seasons since it lost to the All Blacks in the last World Cup final.
"That's a nice little hit of confidence and momentum there for us tonight," said Australia captain Michael Hooper.
"We were controlling them quite well when they had 15 men so when they went down to 14 we didn't need to change much."
Lock Lukhan Salakaia-Loto, scrumhalf Nic White, winger Marika Koroibete and fullback Kurtley Beale also crossed for the Wallabies in front of a packed house of 61,241 at Perth Stadium.
The All Blacks had tries from backs Anton Lienert-Brown, Rieko Ioane, Beauden Barrett and Ngani Laumape but they will not be happy with a defeat on the back of a draw against the Springboks.
"They were very good tonight," said New Zealand skipper Kieran Read.
"The first half was tit-for-tat and we just couldn't get hold of the ball and then they just hit us after halftime and that just really gave them confidence. We have to be better than that."
Australia got off to a blistering start and led by 10 points after as many minutes.
Christian Lealiifano kicked the first points after Ardie Savea was penalized at the breakdown and Hodge got the first try after James O'Connor, starting his first test in six years, offloaded cleverly to set the winger free in space.
The All Blacks hit back with two tries in four minutes to take a 12-10 lead, the first when Lienert-Brown eventually touched down a Jack Goodhue kick through and the second when Ioane finished off a typically clinical move off turnover ball.
Lealiifano kicked his second penalty to put Australia back in front after 27 minutes and the match continued at a frantic pace with the home side playing some of its best rugby for the last four seasons.
The Wallabies pressing for another score just before the break when Barrett crashed into the head of Hooper with a no-arms tackle and became only the fourth All Black to be sent off in a test.
French referee Jerome Garces has been responsible for half of those dismissals having also shown a red card to Sonny Bill Williams for a shoulder charge during the second British and Irish Lions test in 2017.
Lealiifano kicked the penalty awarded to give Australia a 16-12 lead at halftime but nine minutes into the second half the shell-shocked All Blacks were down 26-12.
Salakaia-Loto forced his way over in the corner after 46 minutes before center Samu Kerevi bulldozed down the touchline and got the ball away for White to cross for Australia's third try.
The world champions were not dazed for long, though, and finally got enough possession and pressure to give fullback Beauden Barrett the opportunity to dance his way through the defense and touch down.
Flyhalf Richie Mo'unga added the extras to cut the deficit to 26-19 but Australia continued to press and winger Koroibete nicked the ball out of a tryline ruck to nip over and score a fourth try just after the hour mark.
Hodge crossed for his second after 69 minutes but Laumape replied almost immediately and it was not until Beale skipped over the line with a minute left on the clock that the Australians were able to relax.