Broad took two wickets for just 14 runs in an unbroken 10 overs after England captain Paul Collingwood won the toss.
All-rounder Grant Elliott top-scored witth 56, his maiden ODI fifty which ensuring New Zealand reached the 50th and final over - something that looked unlikely when they were 41 for five in 21.
Elliott, in only his second match at this level, faced 102 balls with three fours before he was caught by Luke Wright after hooking James Anderson.
Together with New Zealand captain Daniel Vettori (18) and Kyle Mills (47) he shared stands of 35 and 54 for the seventh and eighth wickets respectively.
Mills's innings was his career-best and featured two sixes and five fours.
Elliott and Mills were the only batsmen to pass 18.
Broad and fellow quick Chris Tremlett (one for 24), who are both well over 6ft tall each, used their height to get the most out of the pitch.
But it was Anderson who took the key wicket of Brendon McCullum.
The dashing opener intitially took a 16 runs off the first five balls off the third over, including a six flicked over square leg.
But off the sixth ball he was well caught by a leaping Kevin Pietersen at mid-off going for another big shot.
England then put the brakes on dramatically by taking three wickets for five runs in 17 balls to leave New Zealand 42 for four.
Jamie How bottom-edged a pull off Broad into his stumps before Scott Styris gloved a lifting delivery from Tremlett, a replacement for Hampshire colleague Dimitri Mascarenhas, through to wicket-keeper Tim Ambrose.
Ross Taylor and left-hander Daniel Flynn both struggled for runs before they each fell cheaply.
New Zealand, denied the chance of a series-equalling win when Wednesday's match at Edgbaston was controversially called off one over away from a result, went 17 overs without a boundary.
Elliott, who took three for 23 on his ODI debut at Edgbaston after only being called up last week into the squad from south-east English club side Weybridge, ended the drought when he square-cut Wright.
Mills smashed Anderson for six and cleared the ropes again off Wright before he was out off the last ball of the innings.