Allen and Rachin Ravindra put on 100 runs for the second wicket before the wheels soon came off for New Zealand as Allen departed.
Arshdeep made further inroads with two wickets in an over including Ravindra, for 30, and skipper Mitchell Santner, for a duck.
Ish Sodhi hit a valiant 33 off 15 balls before he fell as the last wicket with New Zealand bowled out in 19.4 overs.
Earlier, India lost local boy Sanju Samson for six before Kishan took matters into his own hands in a 137-run third-wicket partnership with skipper Suryakumar Yadav, who hit 63.
Kishan took on leg-spinner Sodhi as he blasted four fours and two sixes in a 29-run 12th over. Suryakumar then reached his third 50 of the series with two successive sixes.
Spinner Santner took down his opposite number when he had Suryakumar stumped, but Kishan raised his hundred off 42 balls with a six, jumping for joy as he soaked up the applause from the fans and dressing room.
Kishan had been dropped by Glenn Phillips in the deep on 84, and eventually fell to Jacob Duffy – ending a knock featuring six fours and 10 sixes. Hardik Pandya kept up the charge though with a 17-ball 42 as India hammered 169 runs off the last 10 overs.
India will begin their T20 World Cup title defence next Saturday when they play the United States in Mumbai.
The Black Caps face Afghanistan in their opening game the following day in Chennai.
- AFP
