Australia were perhaps unlucky the scoreline wasn't wider, but striker Caitlin Foord put in a Matilda of the Match performance scoring a brace.
New Zealand were restricted to very few clear-cut scoring chances of their own, while at the other end some brilliant work by keeper Erin Nayler kept them in the match.
The Matilda's flew out of the blocks and took the lead in just the fifth minute, courtesy of a Caitlin Foord shot from distance.
Chloe Logarzo's dummy on the shot appeared to throw off New Zealand keeper Nayler.
A corner just before half-time led to a frantic goal-mouth scramble that somehow was not tucked away for a Matildas second goal - Michelle Heyman coming closest when she hit the crossbar.
Australia eventually extended their lead shortly into the second half, with Foord shrugging off her marker one-on-one then slotting neatly into the corner to seal her double.
The busy Logarzo had a great chance to put the Matildas up 3-0 in the 61st minute with a well-timed run to meet Heyman's square-ball in the box, but her first-time shot went high and wide.
Substitute Tameka Butt came close to scoring twice towards the end of the match, including a deflected shot in injury time that looped over Nayler but bounced off the crossbar.
A deserved clean sheet and strong performance by Alen Stajcic's side.
Coach Alen Stajcic was full of compliments for Foord who always looked a threat when she was in possession.
"She’s an unbelievable player. You just see how she runs at people, causes problems for opposition defences and if she can add goal scoring to her list of attributes there’s no reason she can’t be one of the best players in the world," he said.
While impressed by patches of the performance, Stajcic said there were still plenty of areas that could be improved on.
"I think our good spells and good passages of play showed that fluency and cohesion that we had in the qualifiers in Japan but I thought we had too many spells where we were a bit sloppy on the ball and gave the ball away too cheaply," he said.
"I think the difference between our good play and our bad play were too great but that can come with not being together for three months and hopefully we improve again on Tuesday. Overall I’m happy but I know we can still improve."
