The Wallabies, who have not won at Auckland's Eden Park since 1986, had a try disallowed in a close first half.
However, winger Julian Savea scored two tries after the break to help the All Blacks dominate the closing stages.
Hooker Dane Coles scored the hosts' sixth try as Australia slipped to their third defeat of the competition.
New Zealand beat the record of 17 straight Test wins set by themselves between 1965 and 1969.
That was matched by South Africa in the late 1990s and the All Blacks again before they were beaten by Australia in 2014.
New Zealand have become the first top-tier nation to win 18 consecutive Tests after beating Australia 37-10 in the Bledisloe Cup.