Beauden Barrett led the charge for the Kiwis scoring four tries to help his side take an unassailable 2-0 lead in the three-match series.
Australia, beaten in Sydney by a huge margin of 38-13 last week, had to win the encounter to keep the series alive.
They stayed in the game for the first 38 minutes as the score read 7-7.
However, a try each by Barrett and Joe Moody catapulted the All Blacks to a 21-7 lead within a space of five minutes.
Barrett converted five of the six All Blacks tries to finish with a match haul of 30 points, a New Zealand individual match record against Australia.
Australia have now lost 22 matches in a row since 2001 in New Zealand and have not won at Eden Park since 1986.
New Zealand coach Steve Hansen called Barrett “a special player”.
“He's been world player of the year for the last two years," he pointed out. "You can’t buy experience and you can’t buy moments in the middle and Beauden’s had those and we saw tonight what happens when they all click together.”
“We got killed on the turnovers. That pretty much sums up the tale,” Australian coach Michael Cheika said.