The Kiwis lost three of their five group games but they received a surprising last-ditch lifeline to the semi-finals just hours earlier on Saturday when Ireland defeated the West Indies by six wickets in Bristol.
Ireland ended a 0-21 losing streak across five tournaments going back 12 years.
"A few of us are now half-Irish," New Zealand veteran Sophie Devine quipped. "(Our) fate is in our hands."
But New Zealand had to topple unbeaten England to head off the West Indies for the second semi-final berth in their group.
After New Zealand put up 3-163, England romped to 1-164 with 16 balls to spare on the back of Danni Wyatt-Hodge's unbeaten 89 in front of 21,018 spectators, a tournament record for a group match.
The other two semi-finalists will be decided on Sunday from Australia, South Africa and India.
Wyatt-Hodge flogged the New Zealand bowlers with her second fifty of the tournament beside her opening-night century.
She's comfortably the event's leading run-scorer with 282 and has smashed the single World Cup runs record of 259 set by Australia's Beth Mooney in 2020 with potentially two more games to play.
Wyatt-Hodge was dropped behind the stumps before she scored in the first over and should have been stumped on 13 but the ball was fumbled.
Her fifty came up from 33 balls, and she finished on 89 not out from 53 balls including 15 boundaries and a six.Â
The defeat closed the international careers of Devine, Suzie Bates and bowler Lea Tahuhu, who combined for nearly 900 appearances for New Zealand.
Ireland go home no longer burdened by their T20 World Cup losing streak, and add to an historic 24 hours for Irish cricket after the men knocked off India for the first time in a T20 in Belfast.
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