Cheap turnover ball in the opening quarter was Australia's Achilles heel with the All Blacks' potent finishers scoring four tries with another thrashing for Schmidt's side on the cards following their humbling last time out in Argentina.
Australia rallied with a score from Fraser McReight before halftime and a Jordie Barrett penalty aside, it was oneway traffic for the hosts in the second period with New Zealand relieved to hear the full-time whistle after nearly capitulating with two late yellow cards.
All Blacks captain Scott Barrett said: "I'm relieved. In the last 15 minutes we found ourselves in a bit of a hole but we hung on with some scramble defence. The game was typical of the Aussies, they don't lie down and showed how desperate they are to get a hand on the Bledisloe Cup.
"We were wounded coming back from South Africa but the players trained really well this week. There was plenty of energy and we started well and showed what we are capable of."
New Zealand coach Scott Robertson said: "We found a way to win, I'm really pleased," he said. "We're getting good experience by winning these tight games. The Wallabies showed a lot of grit, it just shows that any Aussie team you play, they just won't go away."
The All Blacks flew out of the blocks early with Will Jordan making the most of his late switch to full-back after Beauden Barrett's withdrawal by finding a pocket of space and showing his acceleration to score in just the second minute.
The visitors did not let up as they looked to double down on their fast start finding plenty of space down the left side to set up Rieko Ioane for another try in the ninth minute.
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