West Indies were playing for the third straight day after their opening Super Eights match, a 103-run defeat by world champions Australia, spanned Tuesday and Wednesday because of rain.
They made one change from that match, with Lendl Simmons in for fast bowler Jerome Taylor whose 10 wicketless overs against Australia cost 67 runs.
This was New Zealand's first Super Eights match.
The Black Caps were without batsman Lou Vincent who was forced out of the World Cup on Sunday after having his wrist broken batting in the nets against Kiwi fast bowler Shane Bond.
Peter Fulton moved up to open in his place alongside Fleming with Hamish Marshall drafted into the top order barely two days after arriving in Antigua.
Group C winners New Zealand carried forward two points into the second round after beating fellow qualifiers England.
New Zealand: Stephen Fleming (captain), Peter Fulton, Hamish Marshall, Scott Styris, Craig McMillan, Jacob Oram, Brendon McCulllum, Daniel Vettori, James Franklin, Shane Bond and Michael Mason.
West Indies: Chris Gayle, Shivnarine Chanderpaul, Ramnaresh Sarwan, Marlon Samuels, Brian Lara (captain), Dwayne Bravo, Dwayne Smith, Denesh Ramdin, Lendl Simmons, Daren Powell and Corey Collymore.
Umpires: Rudi Koertzen (RSA) and Asad Rauf (Pak).