Australia 505 (Burns 170, Smith 138, Wagner 6-106) and 201 for 3 (Burns 65, Smith 53*, Khawaja 45) beat New Zealand 370 (McCullum 145, Anderson 72, Lyon 3-61) and 335 (Williamson 97, Bird 5-59, Pattinson 4-77) by 7 wickets
Scorecard and ball-by-ball details
At once a benediction and a coronation, Brendon McCullum's final moments as a Test cricketer marked Australia's ascendancy to the world No. 1 Test ranking after a resilient and relentless performance by Steven Smith's men.
It was Smith at the other end as Adam Voges stroked the winning runs through cover after key contributions from Joe Burns and Usman Khawaja. A target of 201 was never enough for New Zealand to defend against an Australian batting line-up that has carried much before them since the harsh lessons of England last year.
Since the nadir of Trent Bridge, Australia have won seven of nine Tests without once tasting defeat, enough to hand them the ICC Mace as the world's top team and a $1 million prize. This was the first time Australia reached No. 1 since 2014, but the difference now was a far younger team aware there was still much more to do: namely to succeed in Asia, against Sri Lanka and India over the coming 15 months.
Befitting their enduring loyalty to McCullum, New Zealand's effort was never less than wholehearted. This was epitomised by Neil Wagner's continued bouncer assault on the tourists, despite carrying what had been revealed to be a broken left hand from a Burns shot that burst through his fingers on the fourth evening.
Even so, it was occasionally puzzling to see New Zealand not really trying to generate pressure through disciplined lines and reverse swing, which Matt Henry in particular was able to find. Smith relished the challenge of matching McCullum's outlandish field settings with creativity of his own.
Khawaja had a fortunate escape in the second over of the morning, edging Trent Boult precisely between the wicketkeeper and a wide sole slip. Thereon he accumulated his runs in calm style.
Batting was more of a struggle for Burns, who was struck one glancing blow on the helmet by Wagner and others on the body. He took 35 minutes of play to add to his overnight score, but refused to be flustered and eventually went to a deserved fifty.
Tim Southee's entry to the attack brought another Khawaja edge, this time held smartly by McCullum above his head. Smith arrived to one last display of lateral captaincy from New Zealand's retiring leader, a packed leg side field and another short-ball attack.
Having been hit hard by a bouncer in the first innings, Smith resolved to attack, and boldly hooked his first short ball from Wagner over the head of the man at fine leg. He used the full width of the crease to open up other scoring zones, and was soon bringing the target well within reach.
After speaking with the umpires, Smith took the opportunity for an extra 15 minutes to try to seal the game without breaking for lunch. Burns rose to the challenge with a pair of boundaries before being bowled by Boult when going for a third, leaving Smith to concede the job could not be done before the interval.
The remaining 16 runs were duly polished off in early afternoon, Voges finishing off the match with a princely cover drive. Australian celebrations were of the reserved variety: partly out of deference for McCullum, but also in acknowledgement of the fact that getting to the top is one thing, staying there quite another.
Daniel Brettig is an assistant editor at ESPNcricinfo. @danbrettig