Brooke Halliday, Lea Tahuhu and keeper Isabella Gaze followed in quick succession soon after.
Otago spinner Eden Carson made a dazzling debut with the ball with the 21-year-old taking 3-31 including the wicket of West Indies captain Hayley Matthews on 46.
Green and Lauren Down contributed a 66-run partnership in the middle order. Down was dismissed on 33 off 56 deliveries after scoring four boundaries with New Zealand on 117-4.
New Zealand openers Suzie Bates and Sophie Devine were out for 16 and seven, while in-form all-rounder Amelia Kerr was caught at point on 21.
The West Indies were unable to build momentum with the bat until Matthews came to the crease. She delivered a captain's knock but was out lbw to Carson.
The next game will be played on Sunday.
New Zealand won the tour opener on Tuesday by five runs in bizarre circumstances under the Duckworth-Lewis scoring system as bad light stopped play.
-RNZ