Stuart Broad took two wickets with the first two balls of a glorious morning to renew belief that the 10 required might be possible on a flat pitch, and debutant spinner Jack Leach was soon in the thick of it too.
But the resistance of Tom Latham (83) and Ish Sodhi (56no), not to mention five dropped chances in New Zealand’s 256-8, left Joe Root’s men with too much to do as the hosts held on bravely for their fourth series success over England - who had to deal with further frustration on top of their 4-0 Ashes trouncing.
Broad provided an astonishing start though England’s rejuvenated ‘enforcer’ could take limited credit when Latham’s opening partner, Jeet Raval, poked a catch straight to square-leg before the majority had taken their seats, or laid the rugs out on Hagley Park’s grass banks.
But it will be fair enough if Broad dines out a few times on the moment he then got his next delivery in the perfect spot to see off Kiwi captain Kane Williamson for his first Test match golden duck in 116 innings of a great career.
To send Williamson packing at the first opportunity, caught-behind on the back-foot defence, was a huge morale boost.
Ross Taylor had not read Broad’s comic-book hero script, blocking the hat-trick ball, but he soon made up for it in the eyes of England followers by instead becoming Leach’s maiden Test wicket.
Dropped in the meantime by James Vince off Broad low at third slip, Taylor mis-swept the slow left-armer to the man who had just been brought up from the boundary to a catching position at backward square-leg.
Like Taylor, Henry Nicholls then fell for 13 too when the returning James Anderson had him feeling for the line pushing forward and edging to slip for Alastair Cook’s second catch of the morning.
England had to wait until after lunch and another 20 overs for their next breakthrough, and it was again a case of Root having his man in position as Mark Wood went round the wicket and struck for the first time in his comeback match when he had the determined BJ Watling flicking a catch straight to Anderson at leg-slip.
It was not until England got Latham, though, that they perhaps appeared to be on the home straight at last.
Vince had more than five hours of playing time in which to regret failing to hold a tough chance at slip when Latham had 23 the previous evening. But he clawed it back when he ran in from the deep to take an ankle-high catch from a mis-sweep at the start of a new spell as Leach switched ends.
Latham’s mistake came after he had kept England at bay for 207 balls, and it left the Kiwis six down with a scheduled 54 overs still left.
Two drops by Mark Stoneman off Leach set the tourists back again, Colin de Grandhomme low at cover on six and Sodhi crucially at silly-point before he had scored in a half-century stand which ate up 26 precious overs.
Wood returned to have de Grandhomme very well-caught low down by Leach this time at fine-leg.
But Sodhi, who dug in for a three-hour 50, and Neil Wagner then would not be moved for 31 overs, whatever England tried - including squad-player ball-boy boundary riders to speed up the over rate and close fielders on their knees to try to make catches out of nothing.
Root himself finally had Wagner caught bat-pad on review at silly-point, but too late from the final ball of the match before bad light had the last word.
Second Test, Christchurch: England 307 (J M Bairstow 101, M A Wood 52, T G Southee 6-62, T A Boult 4-87) & 352-9 dec (J M Vince 76, M D Stoneman 60, J E Root 54, D J Malan 53, C de Grandhomme 4-94), New Zealand 278 (B J Watling 85, C de Grandhomme 72, T G Southee 50, S C J Broad 6-54, J M Anderson 4-76) & 256-8 (T W M Latham 83, I S Sodhi 56 no).
New Zealand drew with England.