The hosts were disappointed by the loss in the opening match of the Women's World Cup in Tauraga
Matthews is stunning with a good shot, making West Indies 259-9 after being asked to hit in ideal conditions at the attractive Bay Oval
And New Zealand are rarely on top of the chase as Matthews claimed 2-41 with an off spin.
After Devine was caught brilliantly and sent in for a 108th by Chinelle Henry, goalkeeper Katey Martin was allowed to set her tail.
Martin's strike brought the equation down to six from the final over, only for Deandra Dottin to pick up the ball for the first time and trap Martin lbw for 44 with a yorker pinpoint.
Dottin then caught Jess Kerr in midway and when Fran Jonas ran out of the next ball, the West Indies won by three rounds.
It was a thrilling curtain-raiser for a tournament delayed by a year by the Covid-19 pandemic, whetting appetite for the 30 games remaining until the final in Christchurch on April 3.
Magic Matthews and Dottin inspire West Indies
Matthews and Dottin were the stars of victory at the 2016 T20 World Cup, but West Indies have been in the shadows of that team ever since – they won just two games at the last 50-over World Cup in 2017.
However, with legendary bowler Courtney Walsh quickly in charge, it was a resurgent display, fueled by Matthews' glorious half.
Together with opening partner Dottin, Matthews immediately hit New Zealand bowling with sweet timing and classic stroke play.
He hit 16 fours and six, receiving support from captain Stafanie Taylor, who made 30, Shemain Campbelle 20 and 36 by Chedean Nation.
West Indies were hampered on the pitch by five dropped catches - two of which saw Devine suspend, who could also have been out - and they looked to have squandered their chance in the face of Martin's late strike.
But Dottin, a great death bowler hampered by a shoulder injury in recent years, dramatically demanded the ball and made a game-winning impact.
Martin was pinned down by a burning swinger, Kerr failed to fall for 25 and 17-year-old Jonas was sent off without a face after being sent back to the non-striker end.
It is a very disappointing result for New Zealand, who are likely to compete with South Africa and India for the two semifinal spots.
But they can take the heart from England in the last World Cup. The hosts suffered a shock loss to India in their first game, only to later be crowned champions.