Joe Root’s men, who fell to a 10th away Test defeat in their last 12 attempts, had scant chance of recovering from the moment they were bowled out for 58 in only 20.4 overs of the first session in this pink-ball series opener.
Almost two days of rain gave them a glimmer of keeping the Kiwis at bay for an improbable stalemate - but after their captain fell to what became the last ball of day four, hopes gradually dwindled on the way to 320 all out in the 127th over of 146 Kane Williamson’s declaration challenged them to bat out.
Stokes (66), in his first Test for more than six months following his enforced Ashes absence this winter, provided most resistance - defying increasing discomfort from his stiff back and needing pain-killers to do so as he dug in for an untypically stoic 13th Test half-century, by far his slowest from 128 balls.
But then, one ball after taking England to 300 in a sixth-wicket stand of 83 with Chris Woakes (52), Stokes’s protracted and theatrical duel with Neil Wagner (3-77) ended with a mishit attempted uppercut at another short delivery and a crucial, running catch by Tim Southee at point.
It was another case of England undoing some much-improved work in their second innings, and a third instance in succession too of a hammer-blow wicket falling to the final ball of a session - this time leaving Woakes with only the tail for company for a further 31.3 scheduled overs.
Unsurprisingly, despite his fourth Test 50 from 109 balls, it proved too much.
Dawid Malan had perhaps represented the most plausible rearguard contender at start of play but, sadly for England, he got no further than the fifth over following an afternoon resumption under sunny skies.
After the left-hander was caught at second slip off Southee to leave England four down and still 227 runs adrift, the tourists ground to a halt for much of the next hour - but did not lose a wicket.
Stokes and Jonny Bairstow both batted against type, refusing to take the bait from a series of wide and full deliveries, as nine overs contained just two runs - and one scoring shot.
Bairstow was fortunate to get off the mark from the 15th ball he faced, and avoid a pair in the match, when he leg-glanced Southee too close to the wicketkeeper - only for BJ Watling to put the chance down.
He was even luckier not to go for 21 when he pulled a Todd Astle long-hop straight to mid-on, where Trent Boult was the culprit this time.
But he failed to heed his warnings, and in the leg-spinner’s next over pulled to midwicket where Williamson leapt high to hold a good catch.
England lost their next big wicket - to the last ball before the break, of course.
Stokes, who had faced the very first ball of the day following Root’s departure, continued his impressive self-restraint.
But Moeen Ali fell lbw to Boult with the second new ball when New Zealand went to DRS which demonstrated pad was hit before bat.
There was increased belief for much of the middle session that England might just grind out an unlikely stalemate, exactly five years to the day since they hung on with nine down at this venue for a famous draw and 0-0 series score.
This time, though, it was not to be as Woakes eventually fell to a short-leg catch off Wagner and then Anderson was last out, poking Astle (3-39) into the hands of mid-off.
Auckland: England 58 (T A Boult 6-32, T G Southee 4-25) & 320 (B A Stokes 66, M D Stoneman 55, C R Woakes 52, J E Root 51), New Zealand 427-8 dec
(H M Nicholls 145 no, K S Williamson 102).