The Kiwi's had appeared to be faltering in their pursuit of 167 before all-rounder Jimmy Nesham smashed a blistering 27 from 11 balls to turn the game on its head.
He lost his wicket off the final ball of the eighteenth over before Daryl Mitchell finished off the innings with two six's and a four from the bowling of Chris Woakes to bring the Black Caps home with seven balls remaining.
Late New Zealand surge stuns England
In the first face-off between the two sides at an ICC tournament since the dramatic 2019 50-over World Cup final - it had looked to be heading for a repeat of the same outcome when Woakes removed both Martin Guptill for 4 and Kane Williamson for 5 inside the opening three overs of the Kiwi's chase. Leaving New Zealand 13-2.
Despite these early losses, a partnership of 82 between Mitchell and Devon Conway helped the Black Caps rebuild - though, the English bowlers were able to keep the scoring in check with the rate close to reaching 12-per-over when Conway was dismissed for 42 in the 14th off the bowling of Liam Livingstone leaving them 95-3.
Livingstone had appeared to have all but won the game for England two overs later when he also removed Glenn Phillips for 2, finishing with impressive figures of 22-2 and leaving New Zealand requiring 60 from the final 29 deliveries.
However, Nesham, who also batted during the super-over of the 2019 final, had other ideas, smashing two sixes during an over worth 23 runs from Chris Jordan as England's bowling began to feel the pressure.
The left-hander continued his onslaught during the following over, hitting Adli Rashid back over his head for six and leaving the Kiwi's on the brink of victory.
England did regain some hope when Nesham finally saw his innings come to a close after chipping one up to Eoin Morgan at extra cover before Mitchell finished things off in devastating style.
The 30-year-old hit Woakes for two consecutive maximums before in the 19th over before closing the innings with a four to the fine-leg boundary, with Mitchell ending on 72 off 47 balls.
English batters fail to reach explosive best despite unbeaten Moeen 50
Despite this, the Three Lions openers got off to a strong start - reaching 37 before Bairstow fell to Adam Milne for 13 in the sixth over.
England's batters failed to find their crushing best throughout the day on what was a difficult wicket at the Sheikh Zayed Stadium and saw their hopes of reaching a truly devastating total slip away when the tournament top run-scorer Jos Buttler lost his wicket for 29 in the ninth - falling lbw to Ish Sodhi.
Moeen Ali, 51 from 37, and Dawid Malan, 41 from 30, took the side through much of the remainder of the innings - eventually reaching 166-4 with the help of some big hitting from Livingstone at the death.
Their total did look a strong one on a helpful pitch for the quick bowlers - though it ultimately proved to be around 20 runs short of a winning score.
New Zealand will now play the winner of the second semi-final at Dubai International Cricket Stadium on Sunday for a chance to win the title.