Chasing West Indies' 139 all out, New Zealand managed 139 for seven, to send the match into a Super Over.
In the Super Over, New Zealand scored 17 runs but West Indies overhauled that target with one ball to spare.
Brief scores:
West Indies: 139 all out in 19.3 overs (Chris Gayle 30, Kieron Pollard 28; Doug Bracewell 3/31, Tim Southee 3/21).
New Zealand: 139 for seven in 20 overs (Ross Taylor not out 62; Sunil Narine 3/20).