After Bates was caught in the deep, Martin was joined by Amy Satterthwaithe and the pair put on 52, with Satterthwaite scoring a breezy 36 off 19 balls.
In reply, the world champions got off to a flyer as Hayley Matthews and Merissa Aguilleira racked up 42 runs for the opening wicket, with Matthews doing the bulk of the scoring.
Matthews continued on to 53 before off-spinner Kasperek removed her via an excellent stumping by Martin.
Stafanie Taylor (51 not out) kept the Windies in the game, and at one stage the visitors needed 15 runs from 10 deliveries.
But Kasperek, bowling the penultimate over, took two more wickets to set up a tense finale, which ended with the West Indies on 159-6.
Kasperek finished with 3-35, while Devine took 2-27.
Game two in the five-match series is at the same venue on Friday night.
- NZN