Chasing a mammoth 308-run target, the visitors never recovered from the body blow suffered in the first eight overs when they lost six wickets for just 41 runs.
A rearguard action by Mathew Wade and James Faulkner, who scored 37 and 36 respectively, only delayed the inevitable as the Australian innings folded for 148 runs in under 25 overs.
Earlier New Zealand batsmen went hammer and tongs on the inexperienced Australian bowling line-up with opening batsman Martin Guptill scoring 90 runs in just 76 balls.
He was ably supported by Captain Brendan McCullum who scored an equally aggressive 44 runs and Henry Nicholls who scored 61.
Though the run rate slowed at the end, the hosts still managed to post a total in excess of 300 runs.
Mitchell Marsh was the pick of the Australian bowlers claiming two wickets for 35 runs. Josh Hazlewood and Faulkner grabbed two wickets as well but both conceded more than 65 runs in their 10 overs.
“Our bowling effort was one of the best we have put out for a while," McCullum said after the match.
His Australian counterpart Steve Smith said that the loss of six wickets in the first 10 overs sealed his team’s fate.
The second game in the series is in Wellington on Saturday.