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.
The Proteas Women have secured a spot in the ICC Women's World Cup semifinals after the game between New Zealand and Pakistan was abandoned because of rain in Colombo.
The first T20 International of England's three match series against New Zealand was abandoned due to steady rain following the completion of the first innings.
Pakistan were in with an opportunity for a massive upset against England at the ICC Women's World Cup but the game was eventually abandoned due to persistent rain in Colombo.
Nat Sciver-Brunt scored a century and Sophie Ecclestone took wickets as England made it three wins from three at the ICC Women's World Cup after beating co-hosts Sri Lanka by 89 runs in Colombo.
