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Australia crushed New Zealand by an innings and 52 runs on day four of the first Test in Wellington.

Resuming on 178-4, trailing by 201, the hosts were unable to make Australia bat again, subsiding to 327 all out and a first home Test loss since March 2012.

Tim Southee hit Nathan Lyon for three sixes in a 23-ball 48 but was caught by Usman Khawaja while attempting another.

Australia will become the world's top-ranked Test side if they win the second and final Test, starting on Saturday.

"We want to be number one in the world in all three formats and I think this Test match is a step in the right direction," Smith said.

Despite the comprehensive nature of the victory, the match was not without controversy, as Australia batsman Adam Voges was on seven before going on to make 239.

Voges was bowled by Doug Bracewell but the delivery was ruled a no-ball by umpire Richard Illingworth - despite TV replays showing that part of Bracewell's foot was behind the crease.

New Zealand captain Brendon McCullum, who made 0 and 10 in his penultimate Test, refused to blame the defeat on the error, but suggested that the TV umpire should be handed the responsibility for calling no-balls.

"Maybe that's something that needs to be looked at, to make sure you get the right decision all the time," he said.

"It's probably easier for an [on-field] umpire to look at the other end rather than having to look down and then look back up.

"But you've got to give credit to Adam as well to have the strength of mind to overcome that and get 239."

Australia's only concern ahead of the next game at Christchurch is a to paceman Peter Siddle, who did not bowl in the second innings.