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Brisbane - Australia crushed New Zealand by 208 runs but the Kiwis were left to curse a disputed decision against skipper Brendon McCullum on the final day of the first Test on Monday.
The Australians claimed the seven remaining wickets on the final morning in Brisbane to go one-up in the three-Test series after dismissing the Black Caps for 295.
New Zealand were chasing a massive 504-run target after two innings declarations from the dominant home side, who easily maintained their 27-year unbeaten streak at the Gabba.
Pugnacious opening batsman David Warner was named man of the match after hitting centuries in both innings as the Australians powered away.
While the Kiwis were well beaten there was controversy over the dismissal of McCullum, who was his team's shining light with a typically free-scoring knock.
McCullum was well set for his first Test century in Australia on 80, when he got a disputed call from English umpire Nigel Llong who gave him out to a catch by Steve Smith at second slip.
McCullum protested, saying he had not hit the ball, but with New Zealand's two referrals already exhausted he trudged from the ground as hopes of staying in the match faded.
"It was a difficult game. I think Australia were outstanding. They played right from ball one, they put us under a lot of pressure," McCullum said.
"We were not quite able to hit our length on the first day, but a lot of that was because of the pressure applied by Dave Warner and from there we were always chasing the game."
Doug Bracewell went next ball, leg before wicket, putting Marsh on a hat-trick which Tim Southee saw off.
But Southee was soon out to another dubious caught behind decision off Josh Hazlewood with the game well and truly gone for the New Zealanders.
Mark Craig and Trent Boult added 46 runs for the last wicket, before Boult was caught behind for 15 leaving Craig unbeaten on 26.
Ross Taylor was the first man out in the fifth over of the final day, gloving an attempted pull shot off Hazlewood to Smith at second slip for 26.
McCullum raised his half-century off 44 balls with a towering straight six off spinner Nathan Lyon and loomed as his team's best hope of avoiding defeat.
James Neesham, who came into bat despite being ruled out for the rest of the series with back trouble, lasted 33 balls before he popped an easy catch to Joe Burns at short leg off Mitchell Johnson for three.
McCullum hoicked Johnson over one of the longest boundaries at backward square leg for his second six to steam into the 70s.
It was McCullum's 97th six in Tests, placing him tied for third all time behind Australia's Adam Gilchrist with 100.
Lyon trapped BJ Watling leg before wicket for 14 with the Kiwi unable to change the umpire's decision as he lost out on his referral.
It then went all downhill at a rapid rate for the Kiwis following McCullum's contentious dismissal, although Craig hit out lustily for the last wicket.
Australia's Smith said it was a "satisfying performance".
"It is a nice way to start the summer to, be up one-nil in a three-match series," he said.
"We still have a few things to work on, I think the new ball bowling we probably let ourselves down a little bit there.
"I think we can hit our length as little bit better and make them play and hit through the covers a little bit earlier in the day, but it is nice to have such a polished performance."
New Zealand's highest successful run chase in the fourth innings remains their 324 against Pakistan in Christchurch in 1994.
