New Zealand had comprehensively won the first four limited-overs games and their 233 in the fifth and final match could have been another winning score.
The visitors began their run chase at a painful crawl to be one for 10 after 10 overs.
But once Daren Ganga and Runako Morton had seen off the new ball attack, the West Indies batsmen gradually reclaimed an air of authority. One-day specialist Wavell Hinds hit the winning run with two balls to spare.
It was a much needed victory for the West Indies, who have not won a one-day match since last August, before the first of three Tests starts here on Thursday.
Going into the final 10 overs, the West Indies still needed 71 runs to win. When captain Shivnarine Chanderpaul fell for 41 in the 43rd over, leaving them 175 for six, they were still staring at a whitewash.
But after Hinds and Denesh Ramdin took the attack to Kyle Mills and Nathan Astle, 17 runs were needed from the final 18 balls, and then three from the last over.
On the third ball Shane Bond had Ramdin caught for 38 with the scores tied, but he could not stop Hinds hitting the winning run off the next delivery to finish unbeaten on 40.
Dwayne Smith had earlier produced a man-of-the-match performance with the ball, taking five for 45 as he ripped through the middle order and tail to restrict the New Zealand total.
Scott Styris overcame a shaky start to provide the backbone of the home innings with 90 after Stephen Fleming won the toss and chose to bat. Fleming contributed 32 and Ross Taylor 31.
Taylor, in only his second One-day International, hit seven quick boundaries before being bowled by Ian Bradshaw. His dismissal reduced New Zealand to 59 for three in the 11th over and brought Styris to the crease.
After a cautious start, which involved a near run-out with Fleming and being dropped by Chris Gayle, Styris stubbornly stayed at the crease.
His timing was not perfect but his concentration and determination to stay in the middle was evident as wickets fell around him.
Styris eventually went in Smith’s last over, leaving the bowler sitting on a hat trick which Kyle Mills avoided.
Scoreboard
NEW ZEALAND:
L. Vincent b Bradshaw 1
S.P. Fleming c Ramdin b Smith 32
N.J. Astle c Ramdin b Edwards 4
R.L. Taylor b Bradshaw 31
S.B. Styris c and b Smith 90
P.G. Fulton c Gayle b Hinds 19
H.J.H. Marshall b Smith 19
B.B. McCullum c Ramdin b Smith 10
J.E.C. Franklin c Taylor b Smith 7
K.D. Mills not out 2
S.E. Bond b Edwards 5
EXTRAS (LB-2, W-8, NB-3) 13
TOTAL (all out, 49.3 overs) 233
FALL OF WKTS: 1-2, 2-8, 3-59, 4-96, 5-146, 6-188, 7-200, 8-224, 9-224.
BOWLING: F.H. Edwards 9.3-0-53-2 (2nb, 3w); Bradshaw 9-1-49-2 (2w); Taylor 7-0-30-0; Gayle 10-0-36-0; Smith 10-0-45-5 (1nb, 2w); Hinds 4-0-18-1.
WEST INDIES:
C.H. Gayle b Bond 2
D. Ganga c Mills b Patel 34
R.S. Morton b Franklin 22
D.J.J. Bravo st McCullum b Astle 38
D.R. Smith c Vincent b Bond 16
S. Chanderpaul c Patel b Mills 41
W.W. Hinds not out 40
D. Ramdin c Styris b Bond 38
R.N. Lewis not out 0
EXTRAS (LB-1, W-1, NB-1) 3
TOTAL (for seven wkts, 49.4 overs) 234
FALL OF WKTS: 1-6, 2-54, 3-72, 4-98, 5-125, 6-175, 7-233.
DID NOT BAT: I.D.R. Bradshaw, J.E. Taylor.
BOWLING: Mills 9-3-37-1 (1nb); Bond 9.4-2-32-3; Franklin 8-0-38-1; Styris 6-0-26-0; J.S. Patel 10-0-58-1; Astle 7-0-42-1 (1w).
UMPIRES: A.L. Hill (New Zealand) and D.J. Harper (Australia).
TV UMPIRE: B.F. Bowden (New Zealand).
MATCH REFEREE: M.J. Proctor (South Africa).
MAN-OF-THE-MATCH: Dwayne Smith.—Agencies