The Black Caps need 150 runs to stay alive at the T20 World Cup.
A fighting half century from Sherfane Rutherford has given the West Indies a solid total to defend after New Zealand had them in serious strife at 76-7.
After suffering a shock loss to Afghanistan in their tournament opener, the Black Caps managed to restrict the West Indies to 149-9.
While Rutherford's innings of 68 from 39 has helped the Windies to a defendable total, they will need to be on song with the ball.
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A must win match for the Black Caps, they have given themselves every chance with a polished display in the field up until the final two overs.
The side made three changes to the eleven which lost its first match, with Tim Southee in for Matt Henry, Jimmy Neesham in for Michael Bracewell and Rachin Ravindra in for Mark Chapman.
Trent Boult and Southee caused the early damage before speedster Lockie Ferguson helped mop up the tail.
It was a superb start for the Kiwis as Boult bowled Johnson Charles for a five ball duck in an opening over which conceded just the one run.
The West Indies were struggling with the pace and bounce of the pitch, taking 13 balls for the first boundary which came from Pooran, an edge flying past third man.
Daryl Mitchell spilled a chance at cover with Pooran on 13, and he immediately made the Kiwis pay with a boundary through mid on.
However, his reprieve wouldn't last long, skying one to Devon Conway behind the stumps who caught it brilliantly over his head to send the skipper walking for 17.
Ferguson then came into the attack and was straight into the wickets, Chase sending one down Ravindra's throat to have them reeling at 21-3.
The wickets kept tumbling, Rovman Powell guiding it straight to Conway after Southee strangled him with three dots on the trot.
Another bowling change brought Jimmy Neesham into the attack, and it brought the first six of the innings, King whacking one over mid off, but his dismissal would come the following delivery.
Pitched on a length outside off, King knicked behind for Conway to take a third sharp catch, this time diving to his right, sending half the West Indies batting lineup to the sheds after just six overs.
A misfield from Kane Williamson marked the first real mistake from the Black Caps in the field as Glenn Phillips was brought on to bowl with the Windies run rate languishing below five.
The hosts took nine from Phillips' first, their best over of the innings to date.
The pair of Rutherford and Akeal Hosein appeared to be building a nice partnership, reaching 28 from 27 before it was broken in soft style, Hosein chipping Mitch Santner straight to Neesham.
His wicket brought the dangerous Andre Russell to the middle, and he made an immediate impact, taking Ferguson for 17, including two big sixes.
The fireworks fizzled fast though as Williamson brought Boult back and Russell skewed a slow ball to Ferguson who swallowed it.
A flurry from Rutherford and Romario Shepherd gave the home side some hope of defendable total, but Ferguson soon trapped Shepherd plumb in front for 13.
Rutherford pushed on but was running out of partners, Boult castleing Alzarri Joseph for six as the hosts lost their ninth and Boult ended with 3 for 16.
Mitchell came on to bowl the 19th and was dispatched for three sixes by Rutherford to rocket the total past 130 and bring up his half century off 33 balls.
Tasked with the final six balls of the innings, Santner went for 18 as the Kiwis conceded 37 in the final 12 balls.