The Black Caps were beaten by England by 20 runs in their latest T20 World Cup game in Brisbane.
New Zealand batsman Glenn Phillips in action Photo: PHOTOSPORT
England made 179 for six and restricted New Zealand to 148 for four.
The New Zealanders will now need to beat Ireland in their last pool game on Friday to secure a place in the semi-finals.
The result also boosts England's chances of making the last four.
England skipper Jos Buttler led by example and smashed 73 while Alex Hales made 52 to power the 2010 champions to 179-6 after electing to bat in the crucial Super 12 contest.
Glenn Phillips threatened to pull off an audacious chase for New Zealand, bashing 62 off 36 balls but had little support from anyone barring skipper Kane Williamson (40).
New Zealand are still top of Group 1 on superior net run rate, followed by England and Australia with all three level on five points.
"You don't become a bad team overnight," Buttler said of their rocky campaign after collecting his player-of-the-match award.
"We had a poor performance, but we've got some great players in our lineup, some really dangerous players and a lot of confidence still in the group.
"I thought we came out tonight and left it all out there."
It was a must-win match for England following their defeat by Ireland and the abandonment of last week's encounter with champions Australia.
Hales accelerated after relatively quiet four overs, hitting Tim Southee for a six and two boundaries in a rematch of last year's semi-finals which New Zealand had won.
Jos Buttler and Chris Woakes celebrate a wicket Photo: PHOTOSPORT
At the other end, Buttler was on eight when he began to walk off after Williamson appeared to have taken a diving catch at cover.
Replays, however, confirmed the ball had burst through the fielder's hands and hit the turf before a tumbling Williamson clutched it against his chest.
Hales fell immediately after completing his fifty and Buttler got another reprieve at 40 when Daryl Mitchell dropped him at deep mid-wicket.
Buttler went on to overtake Eoin Morgan as England's most prolific batsman in T20 Internationals before being run out in the penultimate over.
New Zealand were 66-2 at the halfway stage in their reply and Moeen Ali made a costly mistake dropping Phillips when the batter was on 15.
Phillips, who smashed a century against Sri Lanka on Saturday, gleefully capitalised on the reprieve to reach his fifty in 25 balls.
Ben Stokes broke the 91-run stand when he ended Williamson's run-a-ball knock and England were effectively assured of victory when Phillips holed out in the deep in the 18th over.
Williamson rued the dropped catches that allowed Buttler to pummel the New Zealand attack.
"One of the, if not the, best players in the game, so you don't want to be doing that," he said of his counterpart.
"And if you do he's going to make you pay, and he did that today."
Earlier, former champions Sri Lanka knocked out Afghanistan with a six-wicket victory at the Gabba.
Spinner Wanindu Hasaranga (3-13) led Sri Lanka's disciplined bowling as the Asia champions restricted Afghanistan to a modest 144-8 in the Group 1 contest at Gabba.
Dhananjaya de Silva smashed an unbeaten 64 to help the 2014 champions prevail with nine balls to spare and revive their campaign after back-to-back defeats by Australia and New Zealand.
Sri Lanka now have four points from as many matches, while Afghanistan stay rooted at the bottom with two.
-Reuters
