England hold on to win despite late wobble
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The reigning World Cup champions moved up to fifth on the tournament standings with the narrow victory as they chased down New Zealand's score of 203 at Eden Park with more than two overs remaining.
M19 Match Highlights: New Zealand v England
But they were made to do it the hard way as they lost five wickets for just 20 runs late in the chase to allow a brave New Zealand side back into the contest.
In the end it was experienced bowler Anya Shrubsole (7*) that held her nerve, as the England number 11 found the winning runs off Brooke Halliday (1/18) just as the home side pushed for the final wicket.
Spinners Sophie Ecclestone (3/41) and Charlie Dean (2/36) did the damage with the ball for England, before the experienced heads of Nat Sciver (61) and Heather Knight (42) expertly guided the successful run chase up until the late wobble.
The victory means England's semi-finals prospects are back in their own hands, with wins in their final two matches against Pakistan and Bangladesh likely to see them qualify for the knockout stages.
But New Zealand's hopes are hanging by a thread and their chances of going all the way will largely depend on injuries to skipper Sophie Devine and seamer Lea Tahuhu.
Devine hurt her back while batting on Sunday and didn't take the field for England's innings, while Tahuhu pulled up short and favouring her left hamstring after a delivery.
Sophie Devine retires hurt following injury
It remains to be seen whether the duo will be fit for New Zealand's seventh and final group match against Pakistan on March 26, although the tournament hosts may be out of contention for a semi-final berth by that stage.
Devine's side could still sneak into the final four with a win over Pakistan, but they will be relying on results going their way before that encounter if they are to stay alive.
Opener Suzie Bates (22) was dismissed early and Devine was forced to retire hurt with a back problem in the 15th over, leaving Amelia Kerr (24) and Amy Satterthwaite (24) to negotiate England's spin bowlers.
Kerr was Dean's first victim and wickets continued to tumble late in New Zealand's innings despite the fact Devine bravely returned to the crease to add a further boundary to her score before holing out.
New Zealand's total was never looking likely to be enough, with Tammy Beaumont (25) and Knight using their experience to pace the chase and then Sciver getting involved to put the target within sight.
Frances Mackay (4/34) picked up two wickets in an over as England threatened to self-destruct, but Shrubsole’s experience came to the fore in the final stages to ensure the victory target was reached.
New Zealand XI: Suzie Bates, Sophie Devine (c), Amelia Kerr, Amy Satterthwaite, Maddy Green, Brooke Halliday, Katey Martin, Frances Mackay, Lea Tahuhu, Jess Kerr, Hannah Rowe
**England XI:**Tammy Beaumont, Danni Wyatt, Heather Knight (c), Nat Sciver, Amy Jones, Sophia Dunkley, Katherine Brunt, Sophie Ecclestone, Kate Cross, Charlie Dean, Anya Shrubsole