The Black Caps reached their target in 41 overs after England had been undone by some rash shots and suffered a middle-order collapse on their way to 209 for seven.
If both sides progress to the Super Eight stage as expected, New Zealand will carry over the two points gained from this match.
Their chase began badly however when seamer James Anderson, playing despite a broken little finger on his bowling hand, tempted Lou Vincent to nick behind for a duck in the first over.
Andrew Flintoff then produced a stunning one-handed slip catch to remove Ross Taylor also for nought in the second over.
New Zealand captain Stephen Fleming followed for seven when he played an uncharacteristically wild shot and was caught in the deep by Ed Joyce off Anderson to leave his side in trouble on 19 for three.
Styris and Craig McMillan, who recovered from a bruised toe to play, then repaired the damage before McMillan decided to go after left-arm spinner Monty Panesar's second ball and was caught by Jamie Dalrymple off the cover boundary for 27.
All-rounder Styris was joined by Jacob Oram (63 not out) and the pair guided their side home with a partnership of 138 as England became increasingly ragged in the field.
Heavy morning rain forced the start to be delayed by half an hour, with the wet conditions leading Fleming to put England into bat.
But the bowlers needed little help early on with England's top three getting themselves out with loose shots.
Opener Joyce wafted away from his body and edged James Franklin behind to Brendon McCullum for a duck in the second delivery of the first over after a no-ball.
Ian Bell then made five before making the same mistake against Oram.
Captain Michael Vaughan, who played a full part despite fitness concerns, hit 26 before dragging a Franklin ball on to his stumps.
Kevin Pietersen, who missed most of England's recent tri-series triumph in Australia because of a broken rib, then survived an lbw shout, dropped catch and close stumping to steady the innings with 60 before the mini-collapse left England reeling.
Paul Collingwood (31), Pietersen and Andrew Flintoff (0) fell inside seven balls for one run with New Zealand paceman Shane Bond taking two of the wickets to finish with two for 19 from 10. Styris grabbed two for 25 off seven.
However, an unbeaten eighth-wicket 71-run partnership between Paul Nixon (42) and Liam Plunkett (29) gave England at least something to bowl at and thrilled a half-full Beausejour stadium, which was swelled by ranks of England's Barmy Army.
Kenya hammered Canada by seven wickets in the first Group C match on Wednesday. The seven-week long World Cup culminates in the Barbados final on April 28.