Bairstow cracked an unbeaten 86 and Brook made a rapid 67 as England posted a formidable 198 for four from their 20 overs.
Debutant Gus Atkinson then took a superb 4-20 as the Kiwis slumped to 103 all out in a dismal reply.
Bairstow said: “It wasn't easy at the start, the ball was swinging and sometimes you've got to assess the conditions and then attack when you can. You had to target one of the shorter sides and target your bowlers.
“My injury took me out for quite a long time, I missed quite a lot of cricket.
“It's nice to spend time in the middle, just getting back to the rhythms of white ball cricket,” he said.
“It's different to Test cricket, I'm back opening the batting, all those little things that you sometimes take for granted when you've got a period of time leading in.”
The platform was laid by Bairstow and Brook as the pair put on 131 for the third wicket in a blistering 65 balls.
Bairstow batted throughout the innings, hitting eight fours and four sixes from 60 deliveries while Brook, making another point following his World Cup omission, smashed five maximums in his 36-ball 67.
New Zealand captain Tim Southee bore the brunt of their big-hitting, conceding 23 in one over on his way to figures of
New Zealand’s reply got off to a bad start as Devon Conway chipped to Liam Livingstone at deep square leg to hand Atkinson his first international wicket in the second over.
They slipped to 8-2 as Allen miscued a pull off Sam Curran and was comfortably taken by Jacks.
Glenn Phillips began a recovery but Adil Rashid had him caught on the boundary by Brook for 22 and Mark Chapman, after launching Liam Livingstone for a straight six, then picked out the same fielder.
Daryl Mitchell was caught behind off Brydon Carse, Santner clean bowled by Jacks and Milne reversed swept Rashid into the hands of Ali at slip.
Tim Seifert offered the greatest resistance but he fell for 39 when he sliced Atkinson high into the air and Buttler claimed a steepling catch.
Southee and Ferguson then fell in the same Atkinson over.