New Zealand put themselves under pressure in the test when they were bowled out for 154 in their second innings, where they failed to take advantage of a 51-run first innings lead.
West Indies spinners Narsingh Deonarine (4-37) and Sunil Narine (3-19) did the damage and New Zealand couldn't find an answer.
The Kiwi batsmen will be under the microscope after not a single player scored a century in the series and skipper Ross Taylor said at the post-match presentation they needed to be better.
"It's been a disappointing tour all round, we have had our chances in this match, in several matches this tour," Taylor said.
"The batting needs to take a good hard look at ourselves. There are some positives, the bowlers bowled well on a tough wicket. We needed to set them 270-300 on what was a fourth-day wicket. I think [our batsmen] shouldn't be satisfied with 50-60s, we are a young team, we are getting better every now and then."
West Indies captain Darren Sammy said his side were ecstatic to wrap up the series and praised the efforts of Marlon Samuels who made a crucial 123 in his side's first innings total of 209.
"It's a feeling we are getting used to, and it feels quite good. The way Marlon held the innings together in both innings, that spell from Narsingh yesterday, the performances are coming from different players at different time, that's the hallmark of a good team. We have bowled them out every time we have played them this series, the efforts of Tino [Best] yesterday morning set the tone for us. The next assignment is the World T20, we have gotten the feeling of what it is like to win, but we have to continue to work hard. Last year or two has been tough for us, we are going to celebrate this day, but it is about continuous hard work."
New Zealand's next international assignment is a short tour to India later this month to play two tests and a pair of Twenty20 fixtures.
