McCullum was 92 not out when bad light forced an early tea break on the fourth day with New Zealand 363 for six in their second innings, an overall lead of 61.
He and Daryl Tuffey, on 22 not out, added an unbroken 54 for the seventh wicket as New Zealand showed some welcome fighting spirit after starting today at 187 for five.
McCullum and captain Daniel Vettori, who made 77, added 126, a New Zealand sixth wicket record against Australia, beating Stephen Fleming's and Chris Cairns' 110 here in 1999-2000.
Vettori was the only wicket to fall in the first two sessions when he swept spinner Nathan Hauritz on to his stumps, ending a brave innings of a tick over three hours and 119 balls.
McCullum, meanwhile, reined in his attacking game, reaching his half-century off 110 balls.
At tea he'd batted 208 minutes, faced 172 balls and hit 11 fours and a hooked six off paceman Mitchell Johnson which soared out of the ground.
McCullum also had a big stroke of luck thanks to the Wellington gales recorded at the ground at 130kmh-plus.
On 52 he didn't offer a shot to Hauritz and was given not out by umpire Asad Rauf, but fielding captain Ricky Ponting challenged the decision.
But the Virtual Eye technology which tracks the likely path of the delivery couldn't make a reliable reading from the fixed camera on the wind-blown southern tower, so third umpire Aleem Dar couldn't overrule the decision.
The ball appeared to be heading on to hit the stumps and Ponting remonstrated with the umpires Rauf and Ian Gould. It meant it didn't count as an unsuccessful challenge for Australia, who still had two remaining in the innings.
Australia's bowlers struggled in the wind, with Hauritz doing the bulk of the work as he sent down 48 overs and took three for 118.
Paceman Doug Bollinger, who took a test best five for 28 in the first innings, had two for 65 after bowling just 10 overs in the first two sessions.
