Hughes 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.
Hughes, 21, was recalled to the side in place of the injured Shane Watson who is hoping to recover from a thigh-muscle strain for Saturday's second and final Test in Hamilton.
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Debutant Ryan Harris claimed 4-77 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.
Daryl Tuffey injured
Wicketkeeper Brendon McCullum hit two consecutive boundaries off the bowling of Doug Bollinger (2-80) 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.
The same combination removed Tim Southee (0) and Harris struck in his third consecutive over when he trapped Brent Arnel (3) lbw at 9-396.
Mitchell Johnson (1-107) bowled No.11 Chris Martin for one with Daryl Tuffey left not out 47.
Tuffey didn't take the field to bowl in Australia's second innings' having gone to hospital to have a hand injury x-rayed.
Harris claimed match figures of 6-119 for Australia and spinner Nathan Hauritz took 3-119 from 49 overs in New Zealand's second innings.
