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All Blacks first five-eighth Richie Mo'unga scored two brilliant tries in six first-half minutes and forwards Karl Tu'inukuafe and Dane Coles also crossed as the visitors raced to a 26-0 lead in just half an hour on Saturday night.
The pain eased for the crowd of 25,689 at Sydney's Olympic Stadium early in the second half when Australia first five-eighth Noah Lolesio scored a try on his test debut but Rieko Ioane and Jordie Barrett blew out the score in the last 10 minutes.
The Tri-Nations, which also involves Argentina, replaced the Rugby Championship after world champions South Africa withdrew from the annual southern hemisphere tournament citing player welfare concerns.
The Wallabies had gone into the first test match on Australian soil this year with hopes high but Dave Rennie's inexperienced side made too many errors and were ruthlessly punished for them.
The loss combined with a 16-16 draw and a 27-7 defeat in New Zealand earlier this month handed the All Blacks the Bledisloe Cup with next week's fourth test in Brisbane to spare.
"That trophy means a lot to us," All Blacks captain Sam Cane told reporters. "I'm really proud of the boys, all the hard work we've done and how we've improved every week and I'm really excited about where this group can go."
Australia's young side probably needed everything to go right for them to have a chance of beating the clinical All Blacks but they were on the back foot as early as the third minute.
Filipo Daugunu was shown a yellow card for upending a jumping Caleb Clarke, although he appeared a little unfortunate having been nudged into his fellow winger's path by Cane.
Two minutes later and Tu'inukuafe charged over the Australian line with players unmarked outside him and even if Jordie Barrett was also sent to the sin bin soon afterwards for an elbow to Nic White's face, the All Blacks remained in charge.
The first-five's second came courtesy of a neat chip and chase in midfield and the All Blacks pack drove over the Australia line in the 30th minute for the fourth unanswered try.
A rampaging run from centre Jordan Petaia set up Lolesio's try and gave Australia the first score of the second half but the Wallabies continued to make too many mistakes to mount a serious comeback.
"You can't turn over the ball as often as we did, it puts you under too much pressure," said Australia coach Dave Rennie.
"You have to pay credit to New Zealand, their skillset was outstanding given the conditions. I thought they were top notch and we were a long way off the mark."
Injuries forced Rennie to hand first caps to Lolesio at first five-eighths and Irae Simone at inside centre, but he said inaccuracy throughout the whole team not rookie errors had been behind the defeat.
"We're not going to use that as an excuse, we prepared well, you just can't the ball over as often as we did," he told reporters after his third game in charge.
"We got caught pushing passes. What we talked about at half time was just trying to build some pressure and for 20 minutes we actually played really well.
"But 20 minutes of competitive footy is nowhere near enough against the All Blacks. There was certainly a gulf between the two performances tonight."