It was the Wallabies' first win over New Zealand since 2017.
Barrett's contact with Hopper at the breakdown was reviewed at length by referee Jerome Garces before the referee came to the decision that the lock's "shoulder and elbow on the neck" was "clearly risky, direct and with force".
The six-try victory equalled their biggest-ever winning margin against New Zealand.
The Wallabies entered Saturday's match trailing both the All Blacks and South Africa in the standings but, with the Springboks in action later on Saturday, Michael Cheika's men moved into pole position with a 47-26 success, which marks New Zealand's joint-heaviest defeat and the most points they have conceded in a Test to Australia.
Cheika said the fact that they faced an undermanned All Blacks didn't take any gloss off the win.
Steve Hansen has denied being concerned by the All Blacks' lack of form in the last three Tests as they bid to save the Bledisloe Cup at Eden Park this weekend without injured centre Jack Goodhue.
"They haven't lost to Australia at Eden Park since 1986, they haven't lost a test there since 1994, but that's not going to win the test match for them".
"We were just starting to come right defensively".
Australia played particularly well and deserved the win.
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She added: "But there were chances where she hit shorter balls, but I wasn't expecting her to, so I didn't move up in time ". Beating the world's No. 1 player on Friday is pretty good sign that she is ready to go.
All Blacks fullback Beauden Barrett indicated his younger brother was grappling with his clumsy attempted tackle on Hooper, and subsequent punishment, which now leaves his initial World Cup fate in the hands of the judiciary.
Gareth Davies said the game is more than just a friendly.
"This Aussie side is a pretty good side so we're going to have to step up to the plate".
"Those great All Black World Cup loose forwards of not long ago, McCaw and Jerome Kaino, didn't bother with pointless cheap shots, an attitude which worked".
But the All Blacks responded as they always seem to do with 41-13 scoreline to set themselves on course for Rugby World Cup glory.
"They're still, in my eyes, the number one team in the world - I don't care what the world ranking says", he said.
Although, let's face it, not even the most one-eyed, optimistic, leather-arm-patched Wallabies tragic turned on Saturday night's game thinking we would need some ridiculously arbitrary ICC-style decider to settle this year's series.
He said the Wallabies must improve, just as the home side would.