Salt and Brook reached a century partnership from only 54 balls and provided the momentum as England made 236-4 after being sent in, the highest-ever T20 international score on Hagley Oval.
Tom Banton rounded off the England innings with an unbeaten 29 from 12 balls.
Adil Rashid then took 4-32 as New Zealand was bowled out for 171 in 18 overs, attempting the highest successful run chase in the history of T20 internationals.
It was Rashid’s fourth four-wicket bags in T20s and marked the 21st consecutive T20 innings in which he has taken at least one wicket.
Tim Seifert made 39 and Mitchell Santner 36 as New Zealand lost all 10 wickets to catches.
“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. “The other night the pitch had a little more live grass on it.
“The sun has probably helped us out and made the pitch a little bit flatter and easier for the batters.” The match took place on the same pitch on which the first of the three-game series was intended to be played but was rained-out on Saturday.