The Jamaican opener continued his impressive return to West Indies colours after 12 months out as he lit up his home ground in signature style, slapping nine sixes on way to 125 from 107 balls.
Marlon Samuels also reached three figures with an equally vital unbeaten 101 - his first ODI hundred since 2006 - as the hosts posted 315 for five.
It was a score New Zealand failed to chase with any conviction, despite half-centuries from BJ Watling, Martin Guptill and Kane Williamson, before they were eventually bowled out for 260.
Victory gave West Indies a 2-0 lead in a five-match series they can wrap up in St Kitts on Wednesday.
Ravi Rampaul was the pick of the Windies' bowlers, taking three for 50 including the early dismissal of Rob Nicol (15) as the hosts kept New Zealand comfortably below the asking rate in the early overs.