The New Zealanders suffered a major batting collapse as they chased 164 runs for victory.
England made 163-6 with Jos Buttler top scoring with 73, while New Zealand were bowled out for 150 in the 20th over.
After winning the toss and deciding to bowl first the Black Caps had immediate success with Jason Roy bowled by Tim Southee off the very first ball.
Buttler then steadied the ship making 73, while Jonny Bairstow made 30.
Out of form captain Eion Morgan came in after missing their last game and was given out to a contentious lbw appeal after making 10.
Leg spinner Ish Sodhi took three wickets for 26 runs from his four overs, while Southee, Lockie Ferguson and Glenn Phillips took one wicket each.
In reply New Zealand started well with Martin Guptill making 41 and Devon Conway 20 but there was very little else apart from a flurry from their last two batsmen, Ish Sodhi who made 25 and Todd Astle 16.
Ferguson said at the halfway mark the Black Caps were "very confident " of chasing down England's score but then New Zealand fell from 81-2 to 103-9.
Mark Wood took four wickets and Adil Rashid three.
Guptill launched the first ball of the innings for six , which impressed Ferguson and he hoped it would be a sign of things to come.
"I think when you have your senior player stamping his authority early on in a game like that, hitting a six off the first ball in every game I'd love to see that, but in the field as well even in a warm-up game he was attacking every ball, firing it in, putting in the yards for the lads so when you have that leadership within the group it filters out into the other players but it's always nice to see Guppy in some fine form hitting sixes straight down the ground," Ferguson said.
Ferguson also paid particular tribute to Sodhi's contributions with bat and ball.
"It's always nice to see Ish hit a couple of dingers at the end, his batting is in nice touch and he bowled very well today so he should be pretty stoked about going into the comp with that sort of form."
Despite losing back-to-back warm-up games against Australia and England, Ferguson believed the team would be ready for their opening match of the tournament against Pakistan next Wednesday.
In another warm-up match India beat Australia by eight wickets.
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