After being out in to bat at the toss, Salt struck 85 from 56 balls while Brook smashed 78 off just 35 deliveries as the visitors amassed a total of 236-4 in their 20 overs.
Th Black Caps could only muster 171 all out in reply with spinner Rashid the destroyer-in-chief with figures of 4-32 in four overs.
Salt and Brook shared in a brutal partnership of 129 from just 69 deliveries while Tom Baton finished off the innings with a quick-fire 29 not out from 12 balls to set a record total for a T20I at the Hagley Oval.
The home team lost wickets at regular intervals in the run-chase as England seamers Luke Wood and Brydon Carse striking early in the innings.
Rashid came into his own in the middle overs as the home side's batters were forced to him the spinner in pursuit of a rising required-rate.
The victory means England go 1-0 in the three-match series with one game left to play after the first match was abandoned due to rain.
England opener Ben Duckett says the batting line-up is finding the necessary balance between being attacking and "reckless at times" ahead of the first Ashes Test in Perth on 21 November.
England fast bowler Mark Wood says he wants to up his intensity as he builds up to put himself in the selection frame for the first Ashes Test that starts in Perth on 21 November.
New Zealand legend Kane Williamson has announced his retirement from T20 International cricket with immediate effect to focus on the other two formats of the game.
England's batting frailties came to the fore once again as New Zealand completed a 3-0 series whitewash with a tense two-wicket win in Wellington on Saturday.
