Williamson top-scored with 72 from 46 balls and opener Martin Guptill contributed 65 as the Black Caps battled to a tight victory over England.
The hosts had set a target of 197, and restricted England to 184 for nine in reply.
The result leaves Jos Buttler s men without a win in the series after losses to Australia in their previous two matches.
Buttler put the hosts in after winning the toss, hoping an mottled-looking drop-in pitch with huge bald patches would prove unplayable.
But the gamble backfired as the wicket held up and New Zealand s batsmen finally hit their stride after three straight T20 losses.
“The wicket obviously played a lot better than everyone thought and produced a really good game,” said Buttler, who was standing in as captain for the injured Eoin Morgan.
Williamson said it was a crucial win for New Zealand, who can seal a spot in the final of the triangular series with a win over Australia on Friday in Auckland.
On a personal note, his captain s knock was also rewarding after he had come under fire for a recent lean spell in the shortest form of the game.
“There s been a number of occasions recently when I ve wanted to contribute more, so it was nice to spend some time in the middle today,” he said.
New Zealand s move to shore up the batting also paid off as former Hong Kong international Mark Chapman made a useful cameo of 20 off 13 on his New Zealand debut.
But the target was still achievable given Westpac Stadium s small boundaries, and England shrugged off the early loss of Jason Roy as fellow opener Alex Hales took up the cudgels.
Hales blasted three sixes and six fours in 24 balls to depart on 47, and England looked comfortable as they reached 95 for two.
However when a dawdling James Vince was run out by Williamson, it started a steady stream of wickets that stole England s momentum.
Dawid Malan valiantly tried to revive the innings with 59 off 40 balls, but the only other batsman to offer any resistance was David Willey, whose departure on 21 spelled the end of England s chances.