Ramnaresh Sarwan and Denesh Ramdin last night catapulted the West Indies to a victory they appeared to have blown.
The two joined for an unbroken sixth wicket stand of 48 off just 32 balls. Sarwan was man of the match with a classy 67 from 65 balls, while wicketkeeper Ramdin added a brisk 28 from 18.
In a rain-reduced match - rain and hail stopped play for four hours from 2.30pm - the West Indies chased down the Duckworth-Lewis target of 158 off the second-last ball of the match, after New Zealand laboured to 152-8 from their 28 overs.
In a dramatic finale, Brendon McCullum and Grant Elliott both missed run out opportunities with two runs required for victory. McCullum missed Ramdin when he tried to steal an unlikely single after missing the third ball of Tim Southee's final over.
Off the fourth ball, with two still required, Elliott's shy from backward point just missed running out Sarwan as he took the single that left him needing one from the final two balls. He dispatched the penultimate ball through the infield.
The key over was the one previous, where offspinner Jeetan Patel appeared to lose his grip on the ball and that meant New Zealand lost their grip on the match. Fourteen runs were leaked, as Patel served up a smorgasbord of full tosses.
After Wednesday's series opener in Queenstown was rained out, the West Indies take a 1-0 lead in what is effectively now a four-match series.
The West Indies were handed a huge advantage when rain intervened after 6.5 overs. That meant New Zealand had tailored a quarter of the 28 overs they were eventually allotted for a 50-over approach.
The Duckworth-Lewis revision of six extra runs was hardly enough to redress that balance but the visitors threw away the advantage with some stodgy top-order batting.
Daniel Vettori and Kyle Mills in particular had applied the clamps after Chris Gayle had scored 36 from 31 balls. He had just crushed a flat six off Vettori when he tried to force a flatter delivery and was bowled.
Initially, New Zealand's 152-8 did not appear competitive.
Jesse Ryder (32 from 43), Jamie How (27 from 36) and Jacob Oram (25 from 23) all made starts but real impetus came only at the death when Grant Elliott nudged and occasionally belted his way to 30 not out from 27 balls.
Late last night, New Zealand named an unchanged line up for Wednesday's match in Wellington.