But Paul Collingwood's men go into their last-four clash on Thursday against the runners-up in Group F full of confidence thanks to another authoritative display that made it three Super Eight wins out of three.
Despite having already qualified for the semi-finals, England were determined to maintain their momentum, knowing victory would most likely ensure they avoid Australia in the last four.
And they looked like continuing their superb form with a suffocating display with the ball early on, despite having lost the toss.
Seamer Tim Bresnan set the tone with a tight line and plenty of variation on his pace, and he interrupted a threatening New Zealand opening stand when he bowled Jesse Ryder as the Kiwi swiped across the line of a slower ball.
Brendon McCullum kept New Zealand ticking over with a couple of boundaries, punching Bresnan for successive fours through extra cover before taking on Stuart Broad.
But the Black Caps were rarely much above a run-a-ball in the first 10 overs, and Broad took a superb catch just inside the boundary rope to get rid of Aaron Redmond before Michael Lumb took a far simpler catch to account for key man McCullum - both off spinner Graeme Swann.
However, Scott Styris and Ross Taylor hit the accelerator in fine fashion.
Both were happy to milk the ones and twos on the big Beausejour ground, but mixed in the odd big hit to ensure they consistently hit 10 or more off the over, with Styris, the main aggressor, crunching Ryan Sidebottom back over his head and Taylor slog-sweeping Swann for a maximum.
The pair put on 62 runs in 41 balls before Styris tried one hit too many as he top-edged to Wright sprinting in from the boundary, and Gareth Hopkins chopped on to depart for a single soon after.
Taylor also departed one ball after slogging Sidebottom over the midwicket boundary as he holed out to Bresnan, and a tight final over from Bresnan restricted the Kiwis to 149-6 when, at one point, it looked like they might target 160-170.
Still, as proved earlier in the day by Pakistan, a total of around 150 was certainly defendable and England were desperate to get a fast start in reply.
Craig Kieswetter provided it with a six and a four off Nathan McCullum's opening over of spin, and after he departed caught inside the circle at extra cover attempting another heave, Lumb continued the charge with a series of confident sweeps and drives.
Bresnan, on the back of a fine all-round display, celebrates
However, pace off the ball did for England's top order. Ravi Bopara, in for new dad Kevin Pietersen, failed to make the most of his chance as he slapped Styris straight to cover.
Lumb's frailty against spin was against exposed as he was trapped plumb in front by Daniel Vettori.
Collingwood fell for only three as he spooned a Styris slower ball to midwicket and suddenly England were stuttering.
Step forward Morgan and Wright. The former, playing with impressive calm, lashed Styris over wide long-on with a remarkable one-handed slog, and the latter crashed successive boundaries off Ian Butler on the slog sweep as the pair built a vital half-century stand.
Wright departed for 24 off 17 balls when he holed out at deep square leg, but Morgan and Bresnan continued the push in intelligent fashion, the latter heaving the odd four while the former worked the ball all around the wicket in his unorthodox style.
Morgan eventually fell when Vettori took a fine diving catch at mid-in, and Michael Yardy holed out for a duck at long-on to cause a few jitters.
But Bresnan finished the job in style, pulling away to the mid-wicket fence for four, as England continued their impressive form in the West Indies.
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