Hamish Bennett congratulated on taking a wicket by Martin Guptill
Martin Guptill and Brendon McCullum eased to victory in eight overs, needing only 70 runs to win the match.
Hamish Bennett was the pick of the bowlers, claiming four wickets for just 16 runs to win man of the match.
Kenya never got started with the bat, looking confused against the fast-paced attack of Bennett, Tim Southee and Jacob Oram. Their highest score was 16.
Southee had a chance to claim a hat trick, taking two wickets in two balls, but he lost out when Oram snared the last Kenyan wicket in the 24th over.
Guptill and McCullum chased the runs with a more-than-run-a-ball 39 off 32 and 26 off 17 to finish the match.
The only blemish in the Black Cap innings was when McCullum tried to use the ramp shot to hit the ball over the wicket keeper's head but speared it onto his wickets on a free hit.
New Zealand have had their worries coming into the match, losing miserably against India in their second warmup match by more than 100 runs.
Bowling has been their downfall for both of their warmup matches, allowing Ireland to score 279 in their run chase.
Spinner Nathan McCullum went down with a mysterious bug and was hospitalised a few days before the match, but was fit enough to play the match against Kenya to open the bowling with Southee.
Kyle Mills was out due to a back strain, which has started New Zealand's familiar run of injuries they have every World Cup.
Black Caps next match is against Australia on the 25th, which the ICC has agreed to make a Chappell-Hadlee match.