After the late start because of rain, the game had to finish at 5:56pm local time and at that stage New Zealand was five runs ahead of the West Indies.
New Zealand won the toss and decided to bowl first with Auckland wicket-keeper Izzy Gaze making her debut.
The Windies got through to 29 before losing their first wicket with Rashada Williams dismissed for 19, while fellow opener Natasha McLean made 20.
They were 74 for five after 20 overs before Kyshona Knight and Chinelle Henry came together to put on 83 for the sixth wicket.
Henry top scored with 44, while Knight made 36 with the Windies finishing on 168-7 from their 35 overs.
Spinner Fran Jonas picked up 2-22 from 7 overs, while medium pacer Jess Kerr took 2-29.
Openers Sophie Devine and Suzie Bates got the run chase through to 54 before the captain was dsmissed for 25.
Bates top scored with 51 and her dismisal gave the locals some hope with the runrate increasing to a run a ball.
Amelia Kerr anchored the Ferns innings with an unbeaten 47, while Maddie made 18.
The umpires stopped the game after 33 of the White Ferns 35 overs and it was eventually announced that New Zealand had won the game.
The second of three ODI's is on Friday morning.
The entire ODI and T20 series is being played in Antigua.
-RNZ
