Full-back Israel Dagg claimed the solitary try while Dan Carter did the rest of the damage with the boot, converting Dagg's try and kicking five penalties.
It was not a complete All Blacks performance but it was infinitely superior to Australia, who are now without a win against the Kiwis at Eden Park since 1986.
New Zealand made one change to the side that beat the Wallabies 27-19 in Sydney last weekend, with prop Wyatt Crockett replacing the injured Tony Woodcock.
Quade Copper was back in Australia's side at fly-half but Kurtley Beale was left out of the staring XV.
The home side dominated the opening half but had to wait until the 27th minute to get the scoreboard moving when Carter slotted his first penalty.
Another three points followed minutes later after Australia captain Will Genia was sin-binned for deliberately playing the ball in the ground after making a tackle.
And Carter was accurate again with the boot before the end of the half to give the hosts a 9-0 lead.
It was not all doom and gloom for the Wallabies, who had prevented Dagg from crossing the line twice in the opening period.
However, it took just four minutes of the second half to record the game's only try - shortly after Carter had converted his fourth penalty of the contest.
Sonny Bill Williams tried to make a sprint for the line but then decided to offload to Aaron Smith, who in turn played in Dagg to dot down.
Carter added the extras to make the scores 19-0, and added another penalty after 50 minutes to heap even more misery on the misfiring Wallabies.
Australia had one sustained assault at the New Zealand line soon after when opting to eschew penalty-goal chances to keep the ball in play, but the All Blacks' defence proved sound.