Chasing 167 for victory, New Zealand were in trouble at 13-2 and 107-4 when Jimmy Neesham turned the semi-final on its head with an 11-ball 27 to help achieve the target with one over to spare in Abu Dhabi.
Scorecard | As it happened
With 20 needed off the final 12 balls, Mitchell smashed Chris Woakes for two sixes and a four before his 47-ball blitz triggered wild celebrations in the New Zealand dug out.
New Zealand will face either Australia or Pakistan in Sunday’s final.
They suffered early blows after Woakes struck on the third ball to send Martin Guptill trudging back to the pavilion for four.
(Photo by Francois Nel/Getty Images)
The fast bowler then got skipper Kane Willimson’s prized scalp for five after the batsman attempted a scoop shot to be caught at fine-leg.
Mitchell and Devon Conway put on 82 runs for the third wicket but Liam Livingstone struck with his leg spin to have Conway stumped for 46.
New man Neesham took the bowling head on as he smashed Chris Jordan for two sixes – one of them nearly caught at the boundary by Bairstow but his knee touched the rope – and a four to get 23 runs from the over.
New Zealand are in the final of the #T20WorldCup 2021 🎉#ENGvNZ | https://t.co/zXAsuGVcjZ https://t.co/2PKjPlgTLX
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He finally fell to Adil Rashid’s googly with Eoin Morgan holding on to a catch at extra cover.
Earlier Moeen Ali smashed an unbeaten 51 to steer England to 166-four after being invited to bat as Kiwi skipper Williamson won an all-important toss.
England lost their openers including Jos Buttler for 29, lbw off Ish Sodhi.
But Moeen hit back with his 37-ball knock and put on a key partnership of 63 with Dawid Malan, who hit 41, for the third wicket.
Your @ICC Player of the Match – @dazmitchell47! 72* from 47 to guide the team home. Scorecard |… https://t.co/mkwWuHM0Th
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Pace bowlers Tim Southee and Trent Boult kept a tight leash in the first three overs before Buttler smashed two successive boundaries.
In-form Buttler tried to rebuild but an attempt to reverse sweep leg-spinner Sodhi got him trapped lbw for 29 off 24 deliveries.
The opener, who moved past Pakistan’s Babar Azam as the leading batsman in the tournament with 269 runs, reviewed the call but replays suggested the ball would have hit his off stump.
The left-handed Malan, who was dropped on 10 by wicketkeeper Conway off Neesham, hit the first six of the innings off Southee in the 16th over but departed next ball caught behind.
But Moeen launched an attack as he hit Sodhi for a six and then smashed Milne for two hits over the fence.
Livingstone hit 17 off 10 balls before departing and Moeen completed his first fifty of the tournament with a boundary off Neesham.