West Indies captain Brian Lara had complained about low crowd numbers before the match, but his side did nothing to attract local supporters after another dismal display with the bat led to their second successive Super Eight defeat in two days after losing to Australia by 103 runs in a rain affected match completed yesterday.
"Now we are down to the fighting part of the tournament," said Lara.
"There are four games left and we need to win them all if we are to qualify (for the semi-finals).
"Losing the toss played a small part but we were 60-1 after 15-16 overs and we were in a strong position," added the despondent captain.
"But we lost some quick wickets which set us back again. It looked like a 250-plus track.
"We got some early wickets but when you are defending 177 you need to get 10 wickets to win the match."
New Zealand were spearheaded by in-form paceman Shane Bond who began with a superb spell of seam and swing bowling, removing Windies opener Shivnarine Chanderpaul, caught by Styris for four runs.
Imposing all-rounder Jacob Oram also bowled impressively in a player of the match performance, taking 3 for 23 from eight overs, including three of the Windies top four batsman in Ramnaresh Sarwan (19), Marlon Samuels (9), and Chris Gayle for a well made 44.
Spinner Daniel Vettori also took three scalps, finishing with 3 for 39 off nine overs, while Bond came back to take the wicket of Dwayne Bravo with the first ball of his second spell, caught by Brendon McCullum for 18.
Wicketkeeper McCullum took four catches in the innings, while Bond had figures of 3 for 31 from 8.1 overs.
Lara again played a lone role in the West Indies middle order, after his effort of 77 against Australia yesterday, but was out caught behind to Styris when he tried to accelerate a stagnant scoring rate as wickets fell around him.
West Indies captain Brian Lara looks dejected
as his side struggle in the Super Eights [AFP]
"We bowled really well, we always try to bowl well as a unit," said Oram.
"Shane Bond and Daniel Vettori are our marquee bowlers but the rest of us know what our jobs are and we are capable of knocking over sides like West Indies for 177."
With the small total to chase, New Zealand were always in control even after losing stand-in opener Peter Fulton for a duck off the second ball of the innings, when he was brilliantly bowled by Daren Powell.
Number three batsman Hamish Marshall, who only arrived in the Carribean two days ago as a replacement for the injured Lou Vincent, then made it to 15 before chipping Powell straight to Lara at mid-off to make it 36 for 2.
However, Fleming and Styris then put on a 41-run partnership before the captain was needlessly run-out for 45 by Lara, with McMillan then joining Styris to see New Zealand to an easy win with more than ten overs left to spare.
"We took wickets at key times and kept them to a score which was below par," said Fleming.
"Then we knew that if we batted out the overs we would win.
"We were pretty conservative because we knew that after Daren Powell and Corey Colleymore, the West Indies didn't have a lot of resources."
New Zealand now play Bangladesh in Antigua on April 2, while the West Indies move on to Guyana where they will meet Sri Lanka on April 1.