England 143 and 18 for 2 (Bethell 9*, Root 0*, Southee 1-4, Henry 1-14) need another 640 runs to beat New Zealand 347 and 453 (Williamson 156, Young 60, Mitchell 60, Bethell 3-72)
Kane Williamson's superb century led New Zealand to a gigantic lead over England on a third day which swung from potential tragedy for the tourists to bizarre comedy for all concerned.
"Tragedy" is often misused to describe events which are far from it and probably over-states the hamstring injury which forced Ben Stokes from the field mid-over and kept him out of action for the rest of New Zealand's imposing innings.
But "comedy" perhaps understates the scenes which followed as England, with Ollie Pope standing in for Stokes as captain, resisted taking the second new ball until 13.4 overs after it was due, 1.4 of those bowled by Harry Brook by the time it was delivered to the middle.
Brook had bowled 14 overs in Tests prior to this game, eight on England's previous tour of New Zealand at the start of last year when he claimed his only wicket - Williamson caught behind, no less - and six overs during the 2023 Ashes. The first delivery of this short spell had Mitchell Santner seeing the funny side as he jabbed it away from his face, then grinning some more after he launched a six over long-off four balls later.
Brook sent down two deliveries with the new ball, one of those punched through the covers for four by Tom Blundell, before he was withdrawn from the attack.
England's seamers were undoubtedly tired after their side was bowled out in their first innings for just 143 inside 36 overs and they were a man down without Stokes.
And in fairness, England's spinners took the last six New Zealand wickets to fall - three of them with the second new ball - as left-arm spinner Jacob Bethell claimed his maiden Test wicket and two more to end with 3 for 73.
But it seemed as though the visitors were clutching at straws in the face of Williamson's typically composed 156 in 204 balls which included partnerships of 107 with Rachin Ravindra for the fourth wicket and 92 with Daryl Mitchell for the fifth.
There was nothing funny England could see about the fact that by stumps they had lost both openers with just 18 runs on the board, staring down defeat as they needed 640 more.
Having reached fifty just before the close of the second day with his side already 340 runs ahead, Williamson pressed on through an extended afternoon session after rain had cancelled any play before lunch. He brought up his 33rd Test century - and seventh at Seddon Park - with a thunderous six down the ground and his 150 with a lofted drive over extra cover off Bethell.
Bethell had stepped in to finish Stokes' over and he returned to play a bigger part in the attack after the tea break as Williamson made the most of his chances to score off him and offspinner Shoaib Bashir.
England had their chances against Williamson too. He survived a close lbw decision on umpire's call off Brydon Carse while on 73 with replays showing the ball was ever so close to clipping the bails at the top of leg stump. He was also dropped by Pope on 86 when his attempted pull off Stokes made its way into the glove but the wicketkeeper, leaping a long way down the leg side couldn't hold on. Then, on 106, Williamson edged fine of second slip where Brook wrongly anticipated his shot off Bashir and inadvertently created space for the ball to squeeze through.
But Williamson marshalled the innings expertly when New Zealand resumed on 136 for 3. He and Ravindra added 50 runs in the first 19 overs as the latter exercised greater caution than previously in the series when he unnecessarily chased the ball outside off stump to his peril.
Biding his time in the face of some targeted verbal attacks from England's bowlers, Ravindra started playing some shots midway through the afternoon, including four off the Stokes short ball which caused the England skipper to pull up sore in the same hamstring he injured during the Hundred, leading to two months on the sidelines on that occasion. But Ravindra couldn't follow Williamson to a landmark score - he fell on 44 to a leading edge off Matthew Potts.
Williamson was next man out, his top-edged sweep off Bashir sailing to substitute fielder Rehan Ahmed running round at deep-backward square leg.
Mitchell added 60 off 84 before he holed out to Potts to give Bethell his first, and Glenn Phillips fell cheaply before Blundell and Santner put on another 63 runs for the eighth wicket. Santner unleashed five sixes in his 49 off just 38 balls, but it was the retiring Tim Southee the home crowd wanted to see, giving a huge cheer when he walked out after Santner had slashed Joe Root to backward point.
Desperate to see Southee score the two sixes that would take him to a tally of hundred in his final innings with the bat, they were left disappointed when he holed out trying off Bethell with just two runs next to his name.
Southee wasn't done, however, bowling Ben Duckett in his first over before Matt Henry removed Zak Crawley for the sixth time in as many innings this series, pinned lbw and leaving England rather unamused.