Kane Williamson caused carnage during the powerplay en route to 63 off 39 balls, as the Black Caps raced to 84 for one inside eight overs in Mumbai.
But leg-spinner Rashid slowed New Zealand’s progress, with four wickets falling for 18 runs during the middle overs, to leave England an achievable target to chase in their first warm-up outing.
Reece Topley had made an early breakthrough for England, with Chris Jordan taking a diving catch to remove Martin Guptill for 16.
Williamson and Henry Nicholls then thrashed 65 from 38 balls before the latter fell to Moeen Ali.
However, it was Moeen’s spin partner Rashid who did most the most to stem the flow of runs – having Luke Ronchi caught by skipper Eoin Morgan, fooling Williamson, who was stumped by Jos Buttler after hitting nine fours and a six, and ousting Mitchell Santner during four tidy overs which featured 12 dot balls.
New Zealand’s tail struggled to regain their momentum, with Ben Stokes having Nathan McCullum caught behind, Topley bowling Grant Elliott and Jordan removing Mitchell McClenaghan before Tim Southee thrashed a quick 11 off five balls.