Joe Root top-scored with an impressive 64 -- his 32nd score above fifty in 85 ODIs -- as England posted an all-out score of 310 after being put in to bat.
In reply, New Zealand struggled to overcome the first over loss of Luke Ronchi for a golden duck and, although Kane Williamson struck an assured 87, his team mates were picked off by England's impressive attack.
Liam Plunkett was the pick of the bowlers, taking four wickets as New Zealand subsided to 223 all out in the 45th over.
New Zealand can still reach the semi-finals if they beat Bangladesh in their final game and Australia lose to England.
The day began on a sombre note when play was stopped after six overs at 11am local time (1000 GMT) for a minute's silence to remember the victims of Saturday's militant attack in London.
When play resumed England continued their early progress, although their total would have been higher had their top order not given their wickets away.
IMMACULATE ROOT
Opener Jason Roy, looking horribly out of form, was bowled by a straight ball from Adam Milne for 13 and Alex Hales swept across the line after a quickfire 56 as Milne took another wicket.
When Morgan also departed after a poor shot on 13, England were in danger of stalling.
But Root, who had made a century in England's opening win over Bangladesh, played immaculately, sharing a fourth-wicket stand of 54 with Ben Stokes before bottom-edging Corey Anderson on to his stumps.
Stokes (48) and Jos Buttler (61 not out) kept the scoreboard ticking over before England were dismissed in the 50th over for 310, probably 30 runs short of expectations.
The weather always threatened to make a decisive intervention and a shower in between innings, which delayed New Zealand's reply, made the pitch unpredictable as it dried out.
A stiff wind further complicated matters for batsmen and bowlers alike with groundstaff having to reset the perimeter rope and the bails frequently blowing off.
After the dangerous Martin Guptill departed, edging Stokes to Root for 27, New Zealand's hopes rested firmly on Williamson, who had scored a century in their abandoned opener against Australia.
The No.3 accumulated a solid fifty from 66 balls without ever dominating and was undone by a snorter from Mark Wood which bounced off his gloves to the keeper.
With Ross Taylor departing soon after for 39, and the run rate climbing further, New Zealand's reply subsided as England closed in on a comfortable victory.
(Reporting by Neil Robinson; Editing by Ken Ferris)
