Ireland did well to make it past 200, largely due to George Dockrell's 61-ball 74 and Mark Adair's unbeaten 27 off 15 balls.
Adair then got Ireland off to a stunning start with the ball, claiming Martin Guptill and Will Young for ducks with his first two deliveries.
But Finn Allen and Tom Latham then laid the foundation for the New Zealand chase as both made half-centuries.
The Black Caps still needed a cameo from Bracewell and he was up to the challenge once again, clinching the victory and the series in style with a six over mid-on.
Latham was pleased with the performance and praised the bowling unit.
"Winning the toss was crucial and even though we did, we put the ball in the right areas," the skipper said after the match.
"The guys up top, Matt Henry and Jacob Duffy, set the tone for us getting a couple of early wickets, which is always important in that power play. And obviously the ball was turning as well and I thought the spinners - all three of them - did a fantastic job. To restrict them to 216 was outstanding."
Latham said Allen's 60 runs off 58 balls after losing two early wickets was crucial in the chase.
"Obviously with the bat it was off to a shaky start, but I thought the way Finn came out and played was outstanding. He absorbed a bit of pressure and then put it back on them.
"It was probably similar to that first innings where we couldn't quite get those partnerships together, but we managed to get over the line in the end."
The final ODI of the series is on Friday night before three T20s against Ireland starting next Tuesday.
