The dominant win kept the 50-over series alive after New Zealand found themselves down 2-0 on Sunday having being swept 2-0 in the Twenty20 component of the tour that was played in Florida.
This morning's win at Warner Park in St Kitts was built on the back of a solid batting performance as the visitors posted 249-9 in 50 overs, with Rob Nicol and Nathan McCullum posting half-centuries.
Nicol's 59 earned him the man-of-the-match award and included four fours and three sixes, while BJ Watling scored 40 but a quad strain sustained while running between the wickets meant he didn't take the field in the second innings of the game.
Watling's injury will be assessed during the next 24 hours to gauge the extent of the strain, while youngster Tom Latham kept wicket in Watling's absence.
West Indies opener Chris Gayle has been unstoppable in his past four innings against New Zealand and his wicket was the big one for the visitors to pick up.
Tim Southee delivered when Nicol was involved again and he claimed the catch to send Gayle on his way for 11 and the home side's run chase never gained enough momentum.
No 9 Andre Russell delivered a few lusty blows late in the game to top score with an unbeaten 42 but it was never going to be enough as debutant seamer Trent Boult picked up the final wicket and finished with a tidy 2-45 from 8.3 overs.
New Zealand will likely welcome back Brendon McCullum for the fourth one-dayer on Sunday (NZT) where they will look to square the series and force a decider.
