Vice-Captain Nathan Sealy starred with the ball with 4-21 from nine overs to help the men in maroon restrict New Zealand to 131 all out in just 39.2 overs.
They then needed just 24.5 overs to reach 132-4 thanks to an unbeaten 58-run match-winning partnership between Joshua Dorne and wicket-keeper Jewel Andrew.
Dorne ended up 45* off 66 balls including three fours while Andrew finished 36* off just 24 balls, hitting one four and three sixes.
Jordan Johnson (14) and Steven Wedderburn (10) also chipped in for the Windies.
New Zealand Captain Oscar Jackson took 2-14 from three overs.
The West Indies will take on Nepal in their next warm-up match on Tuesday.
Both teams will enter the match-up at opposite ends of the spectrum so to speak. While the West Indies have looked in splendid form after wins over Nigeria, Australia and England, New Zealand barely made their way into the final eight. The Kiwis managed just a solitary win in three games. After no play was possible in their first fixture against Japan, due to rain, New Zealand defeated Sri Lanka but we then defeated by India. Despite the differences in results to date, West insists the Caribbean team is taking nothing for granted.
“Most of the performances last week were very pleasing but now we are in the knockout stage and it’s about your performance in the last three games of the tournament, rather than the first three games,” West said.
“Certainly, New Zealand are always a very competitive team outstanding in the field and quite creative in terms of their batting and their bowling. They played a reduced overs game against India and at one point they were 100 for 1 off 10 overs with their positive intent at the top of the order. They fell away as spinners took hold but certainly it’s a warning to us in terms of the approach that they have and we’re going to have to match that.”