With the West Indian women needing just 13 runs from the final over of the game, up step experienced veteran Sophie Devine.
Devine was given the ball in the final over of the match, conceding just four runs to give the New Zealanders a 1-0 series lead.
Earlier, captain Suzie Bates continued her good form, falling just one run short of a 50 to set up a great platform for the middle and lower order.
Bates and fellow batswoman Katey Martin put on 76 runs for the second wicket to put the home side in a great position before Bates fell short of her half-century.
That brought Canterbury Magician Amy Sattherthwaite to the crease. The pair put together a 52-run partnership to leave the home side 143-3 with four overs left.
Outstanding death bowling from the West Indian side restricted the White Ferns to just a run a ball in the late over of the White Ferns innings.
With 167 to win, Hayley Matthews opened up the batting for the Windies, smashing the opening bowlers all over Bay Oval to get the visitors off to a quick start.
Matthews top scored for the visitors with 53, while skipper Stafanie Taylor also notched up a half-century to be unbeaten on 51.
Unfortunately for the two, their scores were the only two of any worth, as the rest of the West Indies struggled to form partnerships.
Leigh Kasperek took three wickets for the home side, while Devine chipped in with two wickets.
The teams will stay in Tauranga for the next game of the series on Friday.
New Zealand 167/5 (Martin 54, Bates 49, Sattherthwaite 36, Dottin 2-23)
West Indies 159/5 (Matthews 53, Taylor 51*, Kasperek 3-35, Devine 2-27)
View the full scorecard here.