With captain Kane Williamson flying to 63 off 39 balls, New Zealand were 78 for one at seven overs, but 101 for two at 10 became 123 for five at 15, as the batsmen became befuddled.
No one else reached 20, then England openers Jason Roy (55) and Alex Hales (44) got their side into a solid position. They needed 42 off the last four overs, 20 off the last two and wicketkeeper Jos Buttler (24 not out off nine balls) saw them home.
"It's definitely tougher over here against spinners but everyone's got their own game plan against spin, whether using their feet or going back in the box," Santner said. "We're pretty confident with our batters that, confronted with spin, they can play all right."
Santner didn't see the loss as reason for concern.
"It was a good hit-out. Obviously there's aspects we want to work on but good things came out of it. We're pretty happy with the performance."
Out of the two warm-ups, Martin Guptill, Williamson, Colin Munro, Corey Anderson and Grant Elliott got good runs and all the squad had valuable time in the middle.
New Zealand might also be slightly heartened by the sight of South Africa beating India, also in Mumbai by four runs, 196-8 seeing off 192 for three, albeit with several batsmen retiring during the innings.
In other developments, Afghanistan followed their performances at last year's World Cup by qualifying for the tournament proper, comfortably seeing off test nation, but cricketing basket case, Zimbabwe.
New Zealand will have discovered the identity of their fourth and final pool opponent early today when favourites Bangladesh took on Oman.
The New Zealand's women lost their second preparatory match, by 20 runs to England in Chennai, having lost a last-ball thriller to them 24 hours earlier.
Sophie Devine, with 31, provided New Zealand's only success with the bat. The last five wickets folded for 10 runs.
New Zealand's women start their tournament proper against Sri Lanka in New Delhi, also early on Wednesday morning (NZT).
3 Things to note
1 In a spin
New Zealand got an early insight into how to cope with good spin in Indian conditions against England yesterday and didn't exactly emerge with flying colours. Tough tests await, starting with India's class operators in Nagpur early on Wednesday
2 Captain on pace
Kane Williamson got to 63 from only 39 balls. With heavy and more direct hitters all around him in the batting order, Williamson going briskly as well is a welcome sight.
3 Spin twins?
Watch for the composition of New Zealand's bowling attack against India in Nagpur. Three spinners is a stretch but which two of offspinner Nathan McCullum, left armer Mitch Santner and legspinner Ish Sodhi will get the nod?
