Brook (78) and Salt (85) plundered 129 runs from 69 balls to provide the bedrock of England's mammoth 4-236 after being put in to bat on Monday.
New Zealand folded for 171 in reply in 18 overs - with all 10 dismissals through catches - as England grabbed a 1-0 lead heading into the third and final match in Auckland on Thursday.
The series opener between the sides in Christchurch had been washed out on Saturday.
Asked to bat first, England lost Jos Buttler in the second over but Salt and Jacob Bethell (24) scored briskly until the eventful sixth over from Michael Bracewell.
Bethell hit the spinner for two sixes in that 21-run over, which ended with the batter miscuing one to mid-on.
Brook and Salt then tore into the New Zealand attack with sensational power-hitting.
Skipper Brook cleared the ropes five times in a 35-ball blitz that had several hits clattering into or over the Hagley Oval roof.
Tom Banton, who made 29 not out, produced a 12-ball cameo to help England post the highest T20 International total at the venue.
Brydon Carse rattled New Zealand early in their chase, removing Tim Robinson and Rachin Ravindra in his opening over.
Tim Seifert (39) and Mark Chapman (28) offered some resistance but Adil Rashid (4-32) and Liam Dawson (2-38) struck regularly to deny New Zealand any momentum.
"It's always nice to contribute and to do it alongside Salty who has been very successful for us in this era," said Brook who was Player of the Match. "We kept each other clam and composed, manipulated the field and keep them under as much pressure as possible.
"It was exactly what we talked about with the ball. To get another 10 wickets is awesome."
"England were smart with the way they played - hit to the short side and got twos to the big side," said New Zealand skipper Mitchell Santner.
"When you get a 100-run partnership in a T20, it's hard to stop. We threw different options at them but they were able to keep going."
