With the dramatic win, New Zealand have bounced back from two defeats to trail England 2-1 as the five-match series moves to Wellington's Basin Reserve.
Chasing New Zealand's target of 155 for 3, England were cruising to victory after a breakout innings from Maia Bouchier of 71 off 47 balls, which included 11 fours and one six.
She took her side to 127-2 in the 16th over before hitting out off the bowling of Hannah Rowe.
A game-changing run-out from New Zealand's Amelia Kerr saw the England skipper Heather Knight - the best batter of the series so far - head to the pavilion.
New Zealand pulled England back as the visitors lost 6-25 - and the match was set for a tense finish as England needed eight runs off the last over.
White Ferns veteran Suzie Bates was the hero, claiming two wickets for four runs as England fell just shy at 152 for 8.
Devine - captaining the team in T20 internationals for the 50th time - produced a powerful innings of 60 off 37 balls.
Devine came in at 55 for 2 and left after hitting out to a wide full toss from Danielle Gibson off the second to last ball of the innings.
Devine was supported with the bat by Amelia Kerr (44 off 35). Their third-wicket partnership of 99 runs was the second-highest stand by a New Zealand pair against England in a T20.
Opener Bernadine Bezuidenhout scored 34 at the top of the innings to open proceedings for the home side.
The fourth game of five-match series will be played in Wellington on Wednesday.
