New Zealand won the toss and elected to bat with captain Kane Williamson smashing a 63 that included nine fours as the Black Caps made 169 for eight in their 20 overs.
The second highest scorer for New Zealand was Ross Taylor, who finished on 19 not out at the western Indian city's Wankhede Stadium.
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England opener Jason Roy then powered his way to 55 off 36 balls, including seven runs and two sixes, while Alex Hales notched 44 as England reached 170 for four with four balls remaining.
Leg-spinner Adil Rashid was the standout performer of England's bowling attack, grabbing three wickets for just 15 runs.
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