Using a new format to decide the winner, the tourists struck 25 off their extra over used to break the deadlock. New Zealand responded with 15 to lose by 10 runs.
Earlier, chasing New Zealand's 155 for seven, the tourists reached 155 for eight thanks to a single to Sulieman Benn off the last ball bowled by Tim Southee.
The West Indies' run chase was based around a masterful 67 off 41 balls from captain Chris Gayle, while Ross Taylor top-scored for New Zealand with 63 off 50 deliveries.
Result: New Zealand 155-7 (Ross Taylor 63; Chris Gayle 2-16) tied with West Indies 155-8 (Chris Gayle 67; Daniel Vettori 3-16, Jeetan Patel 2-34). West Indies won by 10 runs via a one-over eliminator