New Zealand 307 for 5 (Latham 69, Mitchell 63, Guptill 57, Conway 56, Holder 2-37) beat West Indies 301 for 8 (Mayers 105, Pooran 91, Hope 51, Boult 3-53) by five wickets
Four batters posted half centuries as New Zealand overhauled the West Indies' total of 301 for 8 to win the third ODI on Sunday by five wickets and clinch the series 2-1.
Mitchell was out with the score on 248 in the 42nd over and Latham at 259 in the 44th, with New Zealand still requiring 43 runs. Jimmy Neesham settled the issue with a decisive innings of 34 from 11 deliveries, taking 18 runs from the 45th over bowled by Yannic Cariah.
Neesham hit a six from the bowling of West Indies captain Nicholas Pooran to end the chase with 17 balls remaining.
"It was obviously nice to make a contribution," Latham said. "I think the partnership that Daryl and I were able to make put them under pressure. We set a target of getting to that 40-over mark where we needed a run a ball."
Latham appeared to have erred when he chose to bowl first and as the West Indies flourished in good batting conditions. Kyle Mayers made 105 in a 173-run opening partnership with Shai Hope, and Pooran smashed nine sixes in a rapid 91 for the West Indies.
The pitch proved much better for batting than those on which the West Indies won the first match by five wickets and New Zealand won the second by 50 runs. The highest previous total in the series was New Zealand's 212 in the second match.
Mayers and Hope stayed together for almost 35 overs to shape the West Indies innings. Their partnership ended when Hope was out for 51 off 100 balls and, as often happens with large partnerships, Mayers was out two balls later and without addition to the total. Brandon King fell soon afterwards with the score at 181 for 3 in a sudden reversal for the West Indies.
But Pooran picked up the pace again, posting a half-century from 33 balls. He had hit nine sixes and and four fours from 55 balls when he was out in the 49th over.
Mayers and Hope made a cautious start to the innings as they found the pace of the new pitch, crawling to 24 after 10 overs, negotiating a short rain break in the seventh over.
"I took my time in the powerplay and it gave me the chance to get in. The last two games I got out in the powerplay," Mayers said in a television interview. "It's not every day you bat the powerplay for 20 runs but it worked out well in the end."