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The match was heading for a tight finish before Boult yorked both Chris Jordan and Liam Plunkett to cut England back to 168 for eight and they eventually finished at 184 for nine, New Zealand winning by 12 runs.
New Zealand's 196 for five — having been sent in — equalled the previous highest T20 score on the ground, against Pakistan two years ago.
The result puts New Zealand in second place on the points table for the inaugural Tri-Series contest. Australia are already through to next Wednesday's final at Eden Park.
England, who needed a record score to win, were off to a flier, courtesy of tall opener Alex Hales. He thundered his way to 46 off 20 balls — including 20 off one Trent Boult over — and ensured England were just ahead of the asking rate in the early stages of their chase.
But Hales departed rashly hitting legspinner Ish Sodhi straight to deep mid wicket.
At the 10-over mark, England were 90 for two, seven runs ahead of New Zealand on comparative rate, but then lost James Vince run out by Kane Williamson's direct hit from mid off.
There was an important contribution from lefthander Dawid Malan, who twice reverse swept fours behind point off Sodhi on his way to 59 off 40 balls.
England's stand-in captain Jos Buttler was caught on the long off fence for two by Tim Southee off Sodhi leaving England 109 for four off 12 overs.
Sam Billings miscued a sweep at Mitchell Santner to be caught at short fine leg and the challenge for England grew taller.
Nerves were rattling as Santner then spilled a catch at head height on the long on boundary off Sodhi's final ball, which rebounded for six.
England needed 48 off the last four overs and David Willey briefly threatened. But Boult's double strike was pivotal.
Bustling medium pacer Colin Munro proved a surprise ace with the ball for New Zealand, getting through two tidy overs for just 11. There were two wickets for Sodhi, Santner and Boult.
Earlier, Williamson discovered how much can hinge on one ball. The New Zealand captain went into the game low on T20 runs. His last three T20 innings had produced innings of 0, 9 and 8 off a combined 36 balls against Pakistan and Australia.
First ball he pushed a delivery from fast bowler Mark Wood back down the onside of the pitch, hesitated, then set off for a run. Wood reacted smartly, gathered the ball, turned and threw at the stumps. Williamson was a couple of metres short of his ground. Game over.
But from four metres Wood hurled the ball at the stumps — and missed. He fell to the ground in despair.
Talk about cashing in. Williamson, under some pressure to produce, did just that, making an impressive 72 off only 46 balls as New Zealand, having been sent in, got to 196 for five.
It was a classic situation of a missed opportunity by one player presenting another one to an opponent.
Williamson and opener Martin Guptill put on 82 off nine overs to set up an impressive target for England to chase. Guptill made 65 off 40 balls, his third half century in seven T20 innings this season.
Williamson, who was going at run-a-ball rate from the start, accelerated and by the time he got to 50 for the eighth time in T20s, he'd faced only 34 balls.
There was a third intriguing innings too from new cap Mark Chapman. The young lefthander showed he has a bit about him in his sparky cameo off 20 off13 balls.
A good thing Chapman chipped in too as the premier late innings hitter, Colin de Grandhomme, had gone first ball — spectacularly caught one handed above his head on the long off fence, by Chris Jordan.
Not to forget the other debutant, wicketkeeper Tim Seifert who had time to bang a couple of sixes too, finishing on 14 off six balls.
The small crowd at the Cake Tin had plenty to enjoy, and were probably pleasantly surprised at New Zealand's performance given the look of the pitch.
Unhelpful — for ground staff — weather conditions in Wellington recently, hot and humid, ate away at a large, rectangular shape of the pitch, giving it a bald, weird appearance. Another pitch-shaped chunk of turf was missing out by the boundary square of the pitch, which added to the ugly look to the ground.
''Actually it was all right,'' Guptill said of the pitch. ''It played a lot better than people thought.''
New Zealand's next game in the Tri-Series is against Australia, who are already through to the Eden Park final next week, at Eden Park on Friday night.
Win that and they are through to the final even before facing England a second time in Hamilton next Sunday.