New Zealand 212 (Allen 96, Mitchell 41, Sinclair 4-41) beat West Indies 161 (Cariah 51, Joseph 49, Southee 4-22) by 50 runs (DLS method)
New Zealand made 212 batting first and the West Indies were in dire straits at 27 for 6, potentially facing their lowest-ever total in an ODI, until a long rain break and bold late-order batting changed the course of the match.
When the rain stopped late in the evening at Kensington Oval, West Indies, who were 63 for 7 at the break, were left to chase 212 from only 51 overs.
Joseph fell with the total at 157 for 9 and Cariah was the last man out for 52 with the total at 161 to make Sunday's third ODI the series decider.
Trent Boult and Southee combined to crash through the West Indies top and middle order, leaving the home team six wickets down in the 10th over. Southee finished with 4 for 22 and Boult 3 for 18.
Earlier, Allen fell four runs short of a maiden century as New Zealand overcame the loss of its captain and a stuttering start to post 212 in 48.2 overs.
Skipper Kane Williamson was ruled out with a quad muscle strain suffered in the first match of the three-match series which the West Indies won by five wickets.
Stand-in captain Tom Latham was among three batters to fall early as New Zealand struggled to 31 for 3 in the 10th over. He was out for a three-ball duck while Martin Guptill fell for 3 and Devon Conway for 6.
Allen revived the innings with an 84-run partnership with Daryl Mitchell (41) for the fourth wicket. The pair stayed together for 20 overs to steer New Zealand into a stronger position at 115-4 when Mitchell top-edged an attempted slog over midwicket and was caught at square leg.
New Zealand failed to build from the promising position. Allrounder Michael Bracewell (6) and the power hitters Phillips (9) and Neesham (1) came and went quickly.
Allen finally was out for 96 on the first ball of the 41st over when New Zealand were 165 for 7. He had faced 117 balls and hit three sixes and seven fours.
"It was nice to get the team off to what we thought was a competitive total," Allen said after the match. "I was disappointed to leave us about 10 overs short. I thought there were stills a few runs out there which we could have put on the seal the deal a bit more."
The New Zealand innings again lost direction in his absence, though Mitchell Santner made an effort to rally the tail. He found an able partner in Boult who stayed with him for five overs during which the pair added a valuable 31 for the last wicket, guiding New Zealand past their total of 190 which proved inadequate in the first match.
Boult finally was out for 16, giving offspinner Sinclair his fourth wicket of the innings. Sinclair finished with 4 for 41 as spinners shared six wickets.