A solid innings of 47 by returning captain Kane Williamson and a dashing 33 from 15 balls by Jimmy Neesham has propelled New Zealand to a 13-run win over the West Indies in the first of three Twenty20 cricket internationals in Kingston, Jamaica.

Neesham struck three fours from the last three balls and 23 runs from the last over of the innings as New Zealand made 5-185 after being sent in to bat at Sabina Park on Wednesday.

Left-arm spinner Mitchell Santner took 3-19 as New Zealand restricted the hosts to 7-172 in 20 overs.

"There was a lot of spin which was a big surprise," Santner, who was voted player of the match, said.

"I think the lengths are key against these guys. They can hit you pretty far, so back of a length worked today and as a unit we were able to pick up wickets which was pretty key."

New Zealand's innings had two parts, separated by a lengthy rain break.

Openers Martin Guptill (16) and Devon Conway (43) gave the tourists a strong start, putting on 63 for the first wicket. But the pair fell to consecutive deliveries from Odean Smith, who went on to take career-best T20 figures of 3-32.

The rain came in the 12th over with New Zealand 2-95 and Williamson at the crease with Glenn Phillips. Players were off the field for almost two hours and the Black Caps briefly lost momentum when play resumed.

Williamson re-established the impetus by taking 33 runs off 18 deliveries but was finally out to a brilliant catch on the boundary from Hayden Walsh, who dashed from mid-wicket to pocket a comfortable catch at speed.

Shamarh Brooks anchored the top of the West Indies innings with 42 runs at almost a run a ball. But there was a lack of consistent momentum afterward.

Nicholas Pooran (15), Jason Holder (25) and Rovman Powell (18) all threatened to take control of the game but couldn't carry on.

Romario Shepherd and Smith shared a 50-run partnership from 23 balls for the eighth wicket to fan the West Indies' hopes.

Shepherd struck an unbeaten 31 from 16 balls and Smith 27 from 12 but they came to the last over needing 26 runs and the task proved too much.

"We want to get better as a group but in saying that I was happy with the performances," West Indies captain Pooran said.

"Santner bowled very well and Ish (Sodhi) got away with a few.

"Scores above 175-180 are tricky for us. Unfortunately losing is contagious and we're a losing side at the moment."

The second game of the three-match series also takes place in Kingston on Saturday before the three-match one-day series heads to Bridgetown, Barbados.