Even then, they must hope champions and group leaders Germany do them a favour by beating Argentina.
Great Britain hit back strongly after going behind to Gemma Flynn's tap-in for the Black Sticks.
Pleased as punch: Cullen (right) celebrates her goal
Alex Danson and Crista Cullen scored either side of the break to set up the win, which was secured thanks to some desperate late defending.
Next up for coach Danny Kerry's team are Japan.
'That will be a completely different game from this one against New Zealand,' he said. 'Japan are a very tough team to break down.'
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London gets ready for the Diamond Jubilee - in pictures
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EXCLUSIVE: I won't play with Joey Barton, says Adel Taarabt
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Diamond Jubilee: Boat by boat, here is where to watch the Queen's Thames flotilla - VIDEO
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Duchess of Cambridge is pretty in pink at her first Buckingham Palace garden party
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News pictures of the day
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Locked up and banned: The Tube drunk whose vile racist rant was caught on film (video)
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British housewife facing FIRING SQUAD over Bali drugs smuggling charge was 'neighbour from hell' -
London 2012 Olympics: Raising the bar and the Games haven't even started yet. Price of toasting Team GB is £6 a pint! -
Timebomb ticking in Thames Estuary could put Boris Island plans in jeopardy -
Regent’s Park rapist: Teenage jogger assaulted by stranger in terrifying 7am attack
Why I think doctors are right to strike 
Family pay tribute to the London man who gave his life to save a five-year-old girl from drowning 
Eton schoolboys fly Games flag on Everest 
Horror on the 5.53! Commuter dragged 200 feet after getting hand trapped on train 
Shrimpy's - review 
The O2
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Playing a game-changing role during the Games
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Win a Silverstone track day with Zantac 75
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Celebrate with MARTINI®
This weekend toast one royal with another and make your Jubilee sparkle with a MARTINI Royale.
Rock star
Happy anniversary
Victoria Coren
Summer party
Diamond Jubilee
Glamour Awards
Garden party
First review
Fair-weather goths
Dog save the Queen
