The World Cup holders raced into an 18-3 lead in the opening game of the newly expanded tournament, which now includes Argentina, through tries by Israel Dagg and Cory Jane before veteran lock Nathan Sharpe crossed just before halftime for the Wallabies' only try.
Berrick Barnes' kicking hauled Australia to within five points to leave New Zealand facing an uncomfortable final few minutes but Dan Carter's fifth successful penalty ensured that the All Blacks take pole position ahead of next weekend's return fixture in Auckland.
Defending southern hemisphere champions Australia troubled their trans-Tasman rivals when they had the ball in hand but a raft of missed tackles and a couple of knock-ons at key moments effectively handed the win to the All Blacks.
"You could say its rustiness, who knows," Barnes said. "We're going to have to go back to the drawing board and rectify it. "We've got a long way to go."
Carter kicked 17 points but the biggest difference between the sides in a stop-start match at Sydney's Olympic Stadium was the speed of the ball won by the New Zealand forwards - and the mistakes made by the Wallabies as the black shirts came at them.
New Zealand coach Steve Hansen blamed the mistakes and 28 penalties in the match on the short turnaround for players following the conclusion of the Super 15.
"It's probably not the most perfect game in the world but when you get two sides coming off the breaks we've had, playing at the intensity we're playing, there's going to be errors," Hansen said.
The visitors' solid scrum laid the platform for their first-half tries and only the regular whistling of referee Alain Rolland kept the Wallabies from being even more comprehensively dominated at the set piece.
The score was 3-3 when Sonny Bill Williams ran decoy to let Carter carry the ball away from the scrum to meet the Australia midfield, slipping a delayed pass to Dagg. The fullback tore past opposite number Kurtley Beale on the left touchline and scored in the corner.
The hapless Beale was then culpable for New Zealand's second try, knocking on a kick under no pressure inside his own 22.
The All Blacks sprayed the ball left to right from the resulting scrum and Dagg swiftly deposited the ball in Jane's hands on the right for the winger to score.
"We worked pretty hard but it's not all about the backs, it's about the timing of the delivery particularly from the scrum," assistant coach Ian Foster said. "It got us ahead of their defenders and we took advantage of that."
Australia made a final attack of the half and Digby Ioane powered through only to be hauled down just short. Will Genia popped the ball up off the ground for Sharpe to go over for his eighth try from 106 tests.
Barnes pulled the Wallabies to within eight points with the conversion and the gap was just five points within five minutes of the restart after the flyhalf landed another penalty.
Carter and Barnes then traded kicks before the New Zealand flyhalf restored the cushion with his fourth successful penalty.
Dagg was bundled into touch as he raced in for a second try in the right corner following a break by Liam Messam and Jane spilled just short of the line on the other wing.
The All Blacks looked to be home and dry but Barnes again hauled the Wallabies to within a try and the majority of the 76,877 fans were roaring, only to be silenced as the ball was hacked clear and Carter made the game safe with the final kick of the match.
Having won the last 13 straight matches against Australia at Eden Park, New Zealand will now keep hold of the Bledisloe Cup for a 10th year in a row if they edge out the Wallabies next weekend.