The tourists resumed at 1-70 early today, needing a further 131 runs to defeat New Zealand in Christchurch.
Steve Smith finished 53 not out, ensuring there were no nervous moments for Australia.
Adam Voges struck the winning runs in the fourth over after lunch on day five but it was fitting that Smith was in the middle.
The 26-year-old’s undefeated streak as captain is now 11 Tests – seven of which are wins – and Australia have come on in leaps and bounds since their miserable Ashes campaign in England last year.
The 2-0 series win lifts Smith’s side to the summit of the International Cricket Council’s rankings.
It is the first time Australia have occupied top spot since 2014.
On top of bragging rights, Australia secured a $US1 million ($A1.39 million) cash prize and the ceremonial championship mace.
Joe Burns set the platform with a career-best knock of 170 in Australia’s first innings and backed it by top-scoring in the second dig.
Man-of-the-match Burns was clean bowled on 65 after the umpires delayed taking lunch, departing when his side needed only 22 runs to win.
The opener faced the brunt of NZ paceman Neil Wagner’s bouncer barrage this morning.
Burns copped a glancing blow to the back of his helmet and a painful hit to his shoulder but knuckled down.
The Queenslander weathered it all without taking a risk, only adding to his overnight score of 27 after almost half an hour.
Smith took a more aggressive approach to Wagner’s short-pitched salvo.
Smith slapped the first delivery he faced from Wagner over the fine-leg fence for six.
The skipper unleashed some unorthodox strokes as he continued to treat Wagner with disdain; swatting the ball down the ground at almost every opportunity.
NZ desperately needed quick wickets to have genuine hope of levelling the series and sending Brendon McCullum out a winner.
True to form, McCullum set funky fields.
But it proved proved his undoing in the second over of the day, when the skipper was stationed at floating slip and an edge flew between him and keeper BJ Watling.
Usman Khawaja was on 19 at the time.
Khawaja was finally out edging for 45, with McCullum snaring the catch at first slip.
But Smith stepped up in style, bringing up his half-century in an hour.
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