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Hughes, was recalled to the side in place of the injured Shane Watson, struck 12 fours and one six while Simon Katich played an anchor-man role with his 18 not out from 65 deliveries as Australia reached their target of 106 without loss and with two sessions to spare.
Debutant Ryan Harris took 4/77 in New Zealand's second innings to help Australia bowl New Zealand out for 407 on the final morning.
The Kiwis had resumed on 6-369 and lost their last four wickets for 38 in 50 minutes of play. Brendon McCullum hit two consecutive boundaries off the bowling of Doug Bollinger in the opening over to reach his fifth Test century. But Harris soon had McCullum caught at first slip by Michael Clarke for 104 from 187 balls.
Since losing the Ashes decider at The Oval last August, Australia have racked up an impressive run of six wins and a draw in Test cricket.
New Zealand will be forced into changing their line-up for the final Test against Australia in Hamilton after Daryl Tuffey broke his hand while making an unbeaten 47 in the Black Caps' second innings.
Australian vice-captain Michael Clarke was named man of the match for his career-best 168 in Australia’s first innings of 5(dec)-459.
Skipper Ricky Ponting said he was extremely proud of Clarke for showing his strength of character after receiving plenty of bad publicity following his broken engagement to model Lara Bingle.