All-rounder Wright's 20-ball innings of 42 included three fours and four sixes as England's power-packed batting line-up scored 214 for seven, their highest total in a T20 international.
The 27-year-old Wright then created immense pressure on New Zealand's batsmen as he bowled several dot balls that forced the hosts to take risks, one of which resulted in Martin Guptill blasting the ball straight to Broad at mid-off for 44.
Guptill's wicket in the 13th over was a body blow for New Zealand as the right hander had looked well set to be the batsmen the hosts could build their late-innings assault around.
Broad then chipped in with two wickets in the 15th over, removing James Franklin (eight) and Colin Munro (28) to ensure England's total was well out of reach.
Broad finished with 4-24, his best T20 international figures, while Wright took 2-29 and added a catch as New Zealand made 174-9 off their 20 overs.
The short boundaries straight down the ground, which is primarily configured for rugby, were peppered with a total of 23 sixes dispatched into the stands.
The highest total for sixes in a Twenty20 international was the 24 hit by New Zealand and India in Christchurch 2009, a feat duplicated by Australia and India in Bridgetown a year later.
Eoin Morgan top-scored for England with 46 from 26 balls and combined with Jonny Bairstow (38) in a 81-run partnership off 7.1 overs as England appeared set for a total in excess of 230 on the bouncy drop-in pitch until the stand was broken.
New Zealand did not help their cause in the field by dropping five catches.
