The chase was plucky and entertaining, Alex Hales sprinting to 47 and Dawid Malan reaching 59, but it ultimately amounted to an enjoyable, doomed game of catch-up.
"The wicket obviously played a lot better than everyone thought and produced a really good game", said Buttler, who was standing in as captain for the injured Eoin Morgan.
Experienced Martin Guptill provided a breezy start the side when he smashed 4 boundaries in 5 balls in 2 overs.
"You can write what you like, that's fine", Williamson said.
Williamson's first job was to back up Guptill, who launched Adil Rashid for three slog-swept sixes en route to 65 from 40 balls. Guptil completed his half-century before getting out a full-toss off Rashid.
The fielding highlight for England was a spectacular leaping catch at long off from Chris Jordan to remove Colin de Grandhomme first ball. As opener, the first six overs offered Guptill the chance to free his arms, before settling into what looked to be his second global T20 century.
The visitors had won the toss and put New Zealand in to bat, leaving the skipper satisfied at his team's efforts on what appeared to be a challenging surface.
Jordan eventually parted his stumps but too much damage had been done.
Jason Roy was caught for eight from Tim Southee's first ball in just the second over to be replaced by Malan.
With a stiff target on the board Hales opted for all-out aggression.
Martin Guptill, Colin Munro, Kane Williamson (captain), Mark Chapman, Ross Taylor, Colin de Grandhomme, Tim Seifert, Mitchell Santner, Tim Southee, Ish Sodhi, Trent Boult.
Williamson said it was a crucial win for New Zealand, who can seal a spot in the final of the triangular series with a win over Australia on Friday in Auckland.
Ish Sodhi removed risky looking Hales for 47 as the Kiwis looked strong. He was beginning to feel untouchable but when he went for a repeat in Sodhi's next visit, he fell short and was comfortably held by De Grandhomme. Dawid Malan though continued his vigil as he kept one end intact but Sam Billings wicket in the 15th over did not good to the English side.
Jordan also removed Williamson in an 18th over in which he conceded only three runs. Wood conceded 51 runs from his four overs and Willey too was expensive up front with the new ball. England's match in Hamilton against New Zealand on Sunday would then be embarrassingly meaningless.