"It's a great shift in momentum, hopefully, and we put a few things in to practice in terms of lessons from the other games. It was nice to get a win away in such a pressure game."
It came at a cost, however. Watling strained his quad while batting today and, despite pushing through the pain before being dismissed, didn't take the field in the second innings of the game.
His injury will be further assessed over the next 24 hours but it's likely Brendon McCullum will slot into the side for Sunday's game, which will also be played in St Kitts. Taylor, who injured his shoulder in the first Twenty20 clash in Florida, is an outside chance to return, too.
Strong fielding has been a hallmark of the New Zealand side during the past decade and they relied on that again this morning as they produced three run outs and held four catches.
Debutant left-armer Trent Boult picked up 2-45 from 8.3 overs and Jacob Oram was economical as he claimed 2-22 from seven overs but Tim Southee snared dangerman Chris Gayle and returned 1-14 from six miserly overs.
"[Gayle has] put us away in every game this series so far, so to get him out really boosted the lads in the field and that's where probably things started," Williamson said.
"Trent bowled really well. He executed his plans well. We were discussing them at the top of his run up and he was quite threatening with that new ball."
West Indies' skipper Darren Sammy, who watched his team stumble in their run chase as only No 9 Andre Russell (42 not out) passed 19, said New Zealand were due to deliver.
"I'm not surprised. We are playing against an international team. We expected them to come out and perform," Sammy said.
"We've been winning since the series started in Florida and today, they came out and they out-fielded us and they were much more positive in their approach.
"New Zealand played really well and it was an off day for us and we will basically put it behind us and we are really looking forward to [game four] to just get back to our winning ways, which we've had in the series."