Trailing by 232 runs after the home side had amassed 585, the Kiwis were skittled for 76 in their second innings after lunch on the fourth day.
The margin of defeat was New Zealand's second worst in all Tests against Australia and their paltry total of 76 was their lowest-ever in Australia. Only two batsmen reached double figures and the innings lasted less than three hours.
Fast bowler Glenn McGrath, full of confidence after scoring his maiden half-century with the bat, ripped through the top-order with three early wickets.
Leg spinner Shane Warne wiped out the tail with four for 15 from 10.2 overs and Jason Gillespie and Michael Kasprowicz shared the other three wickets.
McGrath and Gillespie also starred with the bat earlier on Sunday, completing their first Test half-centuries.
Ridiculed as a batting "bunny" throughout his career, McGrath finally silenced his detractors with a career-best 61 after resuming on 54. It was the third highest score by a number 11 batsman in the history of Test cricket.
LAST-WICKET STAND
Gillespie took his overnight score of 43 to 54 not out, sharing a last-wicket partnership of 114 that broke New Zealand's spirits.
The Kiwis could not have made a worse start
McGrath grabbed another wicket in his second over when he trapped Mathew Sinclair leg before wicket for a duck. He then snared captain Stephen Fleming for 11, Justin Langer holding a low catch at third slip.
The fourth wicket fell right on lunch when Scott Styris padded up to Warne without offering a shot and was given out lbw for seven.
New Zealand went to lunch in deep trouble at 42 for four and things did not improve after the resumption.
Nathan Astle departed in the second over when he was caught by Warne off Kasprowicz for 17 and first-innings centurion Jacob Oram fell for eight when he hit the ball off the back of his bat to Matthew Hayden at slip off Warne's bowling.
Brendon McCullum was the victim of a dubious umpiring decision when he was given out caught behind to a ball that hit a crack in the pitch and missed his bat by about 10 centimetres.
Craig McMillan was trapped lbw by Gillespie for nine after surviving an appeal for caught behind off the previous ball that resulted in an angry exchange with Gilchrist.
Warne cleaned up the last two wickets to finish with eight in the match and take his world record tally to 549 scalps.
The second and final Test in the series is in Adelaide starting on November 26.