The record-equalling ninth consecutive ODI victory places them into a seventh World Cup semifinal in 11 editions.
Led by Martin Guptill's unbeaten 237 from 163 balls, New Zealand plundered the West Indian bowling attack to make 393 for six, the country's third-highest ODI innings.
A squadron of willing hitters supplemented Guptill's lead, including Grant Elliott's 27 off 11 balls - the pair made 55 for the fifth wicket in 19 balls.
The batting was reinforced by a thorough bowling and fielding performance led by Trent Boult, with four wickets for 44, and 36-year-old Daniel Vettori channelling ''Air Jordan'' on the third man boundary with a one-handed leap to dismiss Marlon Samuels.
Boult returned to the top of the tournament wicket-taking charts with 19 as the West Indies was dismissed for 250.
Samuels had an unfortunate match. Guptill drove a boundary to start the game but survived a scare third ball. He clipped a low catch off Jerome Taylor to Samuels at square leg - the spill cost 233 further runs.
No West Indies bowling tourniquet could stem the flow as they struggled to hit competitive lengths and Darren Sammy (8-0-38-0) was the only bowler to concede less than a run a ball. Jerome Taylor took three wickets but went for 71 from seven overs.
West Indies heads lowered and shoulders slumped as the innings progressed, including captain Jason Holder, who at times struggled to get his players' attention as demoralisation seeped in.
Guptill gave regular catching practice to the crowd in the latter stages but three scything square cuts provided the best gauge to his early form. His head was stiller than anything you might see carved on Mt Rushmore.
New Zealand's plan to reach the 35th over with three wickets or less down again proved profitable. At that point, it was on 187 for two, moments after Guptill brought up his first century in 111 balls. His second took 41.
The West Indian highlight was Gayle's stoic 61 off 33 as he braved back pain. Gayle used his bottom hand to maximum effect with eight sixes and two fours, meaning running between the wickets was kept to a minimum.
He took 21 off one Vettori over, but Adam Milne eventually enticed him to chop on.
New Zealand's convincing display was not entirely unpredictable. On form, it was expected to dominate, but to this extent? Extraordinary.
It was further evidence uncharted cricketing territory is within its reach.
- Herald on Sunday
