Set a target of 188 to win, the reigning world champions suffered a batting meltdown after star opener Chris Gayle fell cheaply for 12 and were eventually all out for 140 in the 19th over.
But captain Carlos Brathwaite said the real damage was done in New Zealand's final over when Mitchell Santner and Tim Southee plundered 25 off Williams in a wild over that included three no balls.
"For the first 19 overs we bowled as good as we did. But it happens. Kesrick Williams has been the best bowler in the world this calendar year and he just went awry," Brathwaite said.
"But credit to them (New Zealand). Sometimes you have to give credit to the opposition. They bowled with discipline and they fielded really well."
Southee (10 not out), who partnered Santner (23 not out) in the final over run spree, acknowledged that New Zealand needed the bonus runs after struggling to 162 for seven after 19 overs.
"We struggled early on with the bat but the guys hung in there and were able to finish really strongly and then the way we fielded and bowled was exceptional," said Southee with Colin Munro (53) and Glenn Phillips (56), producing the only innings of note.
Debutant Seth Rance sparked the West Indies batting capitulation when he bagged the prized scalp of Gayle and Chadwick Walton (seven) with successive deliveries.
It left the West Indies at two for 19 and they never recovered from the initial setback.
After 16 overs they were 103 for eight when a late slog by Jerome Taylor (20) and Ashley Nurse (not out 20) produced 28 off 12 balls before Rance came back for his final over to end the West Indies innings with six balls to spare.
It continued a miserable tour for the West Indies, who were comprehensively outplayed in the two Tests and three one-day internationals earlier in the month.
The second match in the series is at Mount Maunganui on Monday.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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