Pace bowler Hamish Bennett cleaned up Kenya's top-order, taking four wickets in his first four overs to finish withfigures of 4-16 from five overs to help set up New Zealand for an easy win in Group A.
Tim Southee removed opener Alex Obanda and then picked up another two wickets in the tail-end, ending with figures of 3-13 from six overs.
Jacob Oram lift Southee stranded on a hat-trick, taking the last wicket to give himself three, 3-2 off 2.5 overs.
New Zealand lost the toss, with Kenya opting to bat first at MA Chidambaram Stadium.