They even gave Wales a spanking there in the 1987 World Cup, in a match made famous by Huw Richards becoming the first rugby player in history to be red-carded while unconscious.
The Wallabies, still reeling from the 53-8 drubbing at the hands of a suddenly in-form South Africa, are trying to do something they've never achieved before - win four Tri-Nations matches in the same season. And if they are to win their first Tri-Nations title since 2001, Robbie Deans has to win the battle of the Kiwi coaches.
With many of the current New Zealand side in nappies the last time the All Blacks won a little golden trophy nicknamed "Bill" (those Aussies, huh - you have to hand it to them when it comes to brilliant nicknames), the rugby-mad nation is desperate to win it at home in 2011. Only one scenario is more horrific than New Zealand not winning the World Cup - and that's a New Zealand coach winning the World Cup, but with another country.
The NZRFU took a huge risk when they allowed Graham Henry to be the first All Black coach to keep his job after returning from a World Cup empty-handed. They let Warren Gatland go to Wales, and Deans to Australia. Gatland wins a little something called a Six Nations Grand Slam, and Deans beats the All Blacks in his first attempt.
All Black fans will gladly accept a mediocre couple of seasons if it means the right man is in charge in 2011, and Henry has the perfect opportunity to prove he is that man. But if Henry loses to Deans this Saturday, the knives will be sharpened, aimed and possibly even thrown.
Deans knew he was taking a gamble with his selection against South Africa a fortnight ago - but it must have been like watching an 80-minute car crash as the out-classed Wallabies slumped to the worst Test loss in their history. Everything the Springboks did, turned to gold. Everything the Wallabies did, turned to something you avoid stepping on while out walking.
With one league convert, Timana Tahu, giving a remarkably adept impersonation of a theatre usher in the midfield, Deans has replaced him with Ryan Cross, another former 13-a-side player. Veteran back-rower George Smith replaces an out-of-sorts Phil Waugh to combat the skills of Richie McCaw, and forwards Nathan Sharpe, Al Baxter and Stephen Moore come into a pack that has to match New Zealand at the set-pieces to have a chance of hoisting the silverware.
For his part, Henry is predictably retaining the team that whitewashed the Springboks in Cape Town. As he says: "Every match has been more important than the one before it and this Test decides the championship.
"Australia's last result was out of character and we expect a real battle."
The All Blacks warmed up for the game with a contact training session against Samoa - the score was 100-something versus not much, and completely irrelevant - and the only injury doubt is over replacement prop John Afoa.
The Samoan match didn't prove a lot, but it did provide a lot of practise at finishing off moves, and at that all-important skill of jogging back to halfway. Some fans would say it was almost as much use as resting key players from the Super 14, playing the might of Portugal and Scotland B and then looking puzzled when you lose to France.
But memories of Cardiff 2007 will fade with a win over the old rivals on Saturday.
Well, fade a bit.