The 51-year-old has steered the side to only three wins in 12 Tests. His players were third in the four-team southern hemisphere competition the Rugby Championship and appear well off the pace a year ahead the rugby World Cup.
"I felt we were able to control the game," said New Zealand skipper Kieran Read, whose side will be chasing a third consecutive World Cup in Japan next year. "We showed some great patience with the ball and connected well together. The World Cup is a massive tournament and we have to come prepared next year."
After taking a 17-10 lead into the half-time pause, Barrett and Bernard Foley traded penalties. But at 20-13 New Zealand eventually cut loose. Barrett exchanged slick passes with Ioane to race clear.
Barrett's conversion put the All Blacks up by 14 points at 27-13 and when Silatolu Latu was sent to the sin-bin for a retaliatory slap to Codie Taylor's face it was effectively game over for the Wallabies.
Ben Smith added insult to injury moments later when he found space to dive over and make it 32-13.
Although Australia grabbed a late consolation try through Israel Folau, Ioane completed a man-of-the-match display by scoring his 22nd try in 21 Tests. He collected an outrageous through-the-legs pass from Barrett to score in the corner.
"That certainly wasn't the outcome we were going for," said Australia captain Michael Hooper. "It's a bit of a punch in the face when you come out with a scoreboard like that. Yet again we've given too many opportunities to New Zealand and they're so clinical in those areas."
New Zealand play Japan in Tokyo on 3 November before travelling to Europe to play Tests against England, Ireland and Italy.
"Australia are a formidable opponent and on their day they can play very well," said New Zealand coach Steve Hansen. "It was important that we started the tour with a good performance and we did that."