After four days of bright sunshine, the heavy downpour began at tea on the final day when New Zealand were 79 for four chasing 112 for victory.
After wrapping up the West Indies second innings for 507 before lunch, the modest target appeared a formality despite the forecast rain.
However, the New Zealand batsmen faltered from the start and were rapidly reduced to 44 for four before Ross Taylor and Corey Anderson arrested the slide.
Anderson finished not out 20 with Taylor on 16, and a Test that at one stage looked as if it would be over in four days instead petered out to a draw on the fifth.
"We would have won that, I believe, if it hadn't rained," said a dejected Brendon McCullum who is yet to taste success in 10 Tests since replacing Taylor as captain after their last win in Sri Lanka in November last year.
"It was disappointing to set ourselves up and be 33 short."
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