At stumps on the third day, New Zealand were 178-4 in their second innings, requiring a further 201 to make Australia bat again.
Test debutant Henry Nicholls was not out 31 with McCullum lbw to Marsh in the final over of the day for 10.
Voges' 239 was in part testament to how docile the pitch had become since New Zealand were rolled for 183 inside two sessions on the first day.
For New Zealand there were memories of being on the ropes against India at the same ground two years ago and being rescued by McCullum's triple century.
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The usually big-hitting captain was showing every sign of looking to dig in for a long stay with his 10 coming off 31 before he was out with three balls remaining in the day.
Martin Guptill (45) and Tom Latham put on 81 for the first wicket, New Zealand's best opening stand against Australia since 1993.
It was Voges, though, who ensured Australia had a firm grip on the match.
He resumed the third day at 176 and added a further 63 before his marathon 504 minutes in the middle ended caught and bowled by Mark Craig.
It was 614 runs since he was previously dismissed in the pink-ball Test against New Zealand at Adelaide in November, easily bettering the previous record of 497 between dismissals set by India's Sachin Tendulkar in 2004.
His double century -- coupled with Usman Khawaja's 140 -- also ensured a record first-innings lead for Australia against New Zealand in an innings where six Australians failed to reach double figures.
Latham and Guptill saw off the new ball but when they looked comfortable and settled, Guptill tried to smack off- spinner Lyon out of the ground and was caught by Marsh.
Hazlewood, Australia's chief destroyer in the first innings, tempted Williamson to prod at a ball outside off and it was nicked through to wicketkeeper Peter Nevill.
A huge deficit is a situation New Zealand know well at the Basin Reserve, where they request a green wicket to suit their strike bowlers. But if they lose the toss, the advantage goes to the opposition.
Two years ago it required McCullum's 302 to secure a draw against India after New Zealand trailed by 246 on the first innings.
Pakistan's big hopes rest with their pace attack led by
Wahab Riaz and Mohammad Amir, who is back playing Test cricket after a five-year ban following a spot-fixing controversy in 2010.
"He bowls at good pace, swings the ball, he's got a fast-arm action and knows his game really well for a young bowler.
"So he's one of the guys they're going to rely on to get that ball swinging around and trying to get wickets early and throughout an innings."
Leg-spinner Yasir Shah, who has taken 116 wickets in 20 Tests, injured his back in a pre-Test warm-up game and faces a fitness Test.
The clash will be Australia's third pink-ball Test, but the first under the Brisbane lights, having beaten New Zealand and South Africa in Adelaide. Pakistan downed the West Indies in their only day-night Test in Dubai in October.
Australia (squad) - David Warner, Matt Renshaw, Usman Khawaja, Steve Smith (capt), Peter Handscomb, Nic Maddinson, Matthew Wade, Mitchell Starc, Josh Hazlewood, Nathan Lyon, Jackson Bird, Chadd Sayers.
Pakistan (squad) - Misbah-ul-Haq (capt), Azhar Ali, Sami Aslam, Sharjeel Khan, Younis Khan, Asad Shafiq, Babar Azam, Sarfraz Ahmed, Mohammad Rizwan, Yasir Shah, Mohammad Nawaz, Mohammad Amir, Wahab Riaz, Rahat Ali, Sohail Khan, Imran Khan.
Umpires: Ian Gould (ENG) and Richard Illingworth (ENG)
Third umpire: Sundaram Ravi (IND)
Match referee: Ranjan Madugalle (SRI).