Defending a total of 149 for six, New Zealand's bowlers couldn't contain England's power hitters as they reached their target with five balls to spare when allrounder Tim Bresnan (23 not out) hit Kyle Mills for four.
Eion Morgan blasted 40 off 34 balls in the middle stages to make it safe for England.
It was a disappointing end for New Zealand who scored a thrilling one-run win over Pakistan to stay alive in the tournament, only for Pakistan to reach the semis on net run rate after they beat South Africa by 11 runs earlier today.
With an in-form bowling lineup, New Zealand would have backed themselves to defend their total and progress to the playoffs.
England were missing star batsman Kevin Pietersen who returned home for the birth of his first child, and were already guaranteed a semifinal after beating South Africa and Pakistan.
England openers Craig Kieswetter (15 off 12) and Michael Lumb (32 off 21) flew into their work against new ball pair Nathan McCullum and Shane Bond, and they were well set at 60 for one in the seventh over.
New Zealand held their catches and had a glimmer of hope when they took three for six in 2.1 overs to reduce England to 66 for four; Scott Styris removing Ravi Bopara and captain Paul Collingwood and captain Daniel Vettori dismissing dangerman Lumb lbw.
But Morgan snatched the game away, hitting four fours and a six while Luke Wright (24 off 17) kept the momentum going.
It was New Zealand's most disappointing bowling effort of the tournament, with Styris ending with two for 16 off three and Vettori taking one for 24 off four. Bond recovered to remove Morgan and Wright to end with two for 29 but it was too late.
"We did a great job to fight back and put England under pressure but Morgan and Bresnan's partnership took it away from us," Vettori said.
"We needed to take wickets in clumps and we probably just took them a little too late."
Vettori rued his side's inability to post big totals at the tournament.
"In all formats of the game that has been our problem, we just haven't been able to put enough runs on the board. We've got some really talented batsmen but unfortunately there just weren't enough runs. We fought hard with the ball but it wasn't good enough today."
Vettori batted first on winning the toss on what appeared a dry, slow surface at Beausejour Stadium and addressed their top-order batting concerns by recalling Aaron Redmond for an out-of-sorts Martin Guptill.
New Zealand were teetering at 62 for three in the 11th over after Jesse Ryder (nine) and Redmond (16) departed early, then opener Brendon McCullum took on the long-on boundary off spinner Graeme Swann and lost to end his innings of 33 off 32 balls.
Ross Taylor and Styris rescued the innings with a fourth-wicket stand of 62 off 41 balls, Taylor topscoring with 44 off 33.
After a quiet tournament by his high standards, Taylor hit two sixes in his brisk knock before he departed trying to bring up 50 off paceman Ryan Sidebottom in the 19th over.
Styris chipped in with 31 off 19, including three fours and a six, as New Zealand were about 10 runs short of a par total.
Scores:-
New Zealand 149-6 off 20 overs (R Taylor 44, B McCullum 33, S Styris 31; G Swann 2-31, S Broad 2-33) lost to England 153-7 off 19.1 overs (E Morgan 40, M Lumb 32; Styris 2-16, S Bond 2-29) by three wickets.
