After losing badly to Afghanistan in their first match, and hence getting into a winning position, the Black Caps never developed any momentum and could only manage 136 for nine.
After this defeat, New Zealand needs a miracle to advance from the group stage. If Afghanistan beats Papua New Guinea on Thursday, the Kiwi team will be eliminated.
West Indies pacer Alzari Joseph (4/19) and spinners Gudakesh Moti (3/25) and Akeal Hosein (1/21) kept the home side in control as they registered their third successive win and qualified for the Super Eight stage of the competition with one group match still to play, against Afghanistan in St Lucia on Monday.