Led by Ross Taylor's 16th test century and with fine but windy weather forecast tomorrow, New Zealand are poised to press for a series victory against Pakistan, the world's No.2 side.
The hosts declared at 313 for five, leaving Pakistan to survive three overs before stumps on the fourth day in Hamilton. The visitors finished on one without loss, but the chase for 369 should be insurmountable if past Seddon Park results are a gauge.
In 2000, Australia hauled in the highest successful fourth innings chase with 212-4. The highest score in the final innings was Sri Lanka's 344-6 for a draw in 1991.
If New Zealand secure a draw or win, it will be the first time in 31 years they have triumphed in a series over Pakistan.
Taylor, who undergoes surgery on his left eye this week to remove a pterygium growth, looked as comfortable as he has in months at the crease.
He finished unbeaten on 102, the first time he has passed 50 in 12 test innings. The mark also broke New Zealand's seven-test hundred drought.
Appropriately Taylor reached the milestone cutting backward of point, the signature shot in an innings which brought him to within one ton of mentor Martin Crowe's New Zealand test century record of 17.
Seven boundaries were slapped between point and gully and seven were leg glanced. The speed of his hands and a savage intent made captivating viewing. He leaned forward in his stance, before making a judgement call and rocking back where necessary to attack.
He was dismissed lbw to Riaz on 16 but survived courtesy of a no-ball on review. The ball tracker also showed the delivery going over the stumps.
Earlier, Kane Williamson (42) and Tom Latham (80) forged a 96-run second-wicket partnership, the foundation in establishing the hosts' target.
The pair survived a run out calamity by one television frame in the 19th over. Sub-fielder Yasir Shah picked up and underarmed in one motion towards the striker's end. When he hit the stumps Latham was 'out'; when the bail lifted Latham was 'in'. The opener was 23 and New Zealand 47-1.
Latham was cruelly treated on the verdict. Initially the scoreboard operator posted 'out' on the screen before reverting to 'not out' moments later. Hopefully the culprit is never put in charge of any nuclear warheads.
Williamson was last dismissed in the 40s in June 2014, and had navigated through them 19 times since. Imran Khan delivered a candidate for ball of the day, forcing the New Zealand captain onto the back foot to feather an edge to Sarfraz Ahmed.
Latham passed 50 for the third time in 18 innings at home; he has done so 13 times in 33 innings overseas. It continues a curious pattern to his scoring since the Zimbabwe series in August. Latham has had 13 innings, passed 50 four times and not reached 10 on the other nine occasions.
This innings marked a return to his customary grit until Wahab Riaz, working towards 140km/h, got a short ball to hurry on. Latham lobbed a legside catch to Sarfraz.
Colin de Grandhomme offered late impetus, belting 32 off 21 balls.
New Zealand started the day on 0-0, holding a 55-run lead. At lunch they were 97-1. Jeet Raval practically walked, such was the accuracy of Mohammad Amir's lbw shout.
Amir, Imran and Wahab each delivered accurate spells but Pakistan may have regretted not selecting the world's seventh-ranked bowler Yasir as a point of difference on an ageing wicket.
Imran finished with the best figures of 3-76 from 20.3 overs.