Ross Taylor's 85 and New Zealand's progress to the World Cup's Super 8 stage was tempered Tuesday by a hamstring strain that kept him off the field in Kenya's innings.
Taylor hurt his right hamstring and needed a runner late in his innings that helped propel New Zealand to 331 for seven against Kenya, its highest World Cup total.
Skipper Stephen Fleming (60), Scott Styris (63) and Craig McMillan (71 from 48 balls) contributed half centuries, and New Zealand added 100 runs in the last 10 overs.
Kenya was all out for 183, giving New Zealand a 148-run win to go with its opening six-wicket win over England in the pivotal Group C match.
Kenya's reply started badly, openers David Obuya out lbw in the third over and Maurice Ouma run out in the sixth as their team slumped to 8 for two.
Ravi Shah went to the crease in the third over and anchored the innings with 71 while wickets fell steadily at the other end. Kenya can still qualify for the Super 8s with a win over England on Saturday. New Zealand takes on last-place Canada on Thursday in its last Group C match.
Lou Vincent, Stephen Fleming (captain), Ross Taylor, Scott Styris, Craig McMillan, Jacob Oram, Brendon McCullum (wicketkeper), Daniel Vettori, James Franklin, Shane Bond, Michael Mason.
Maurice Ouma (wicketkeeper), David Obuya, Ravi Shah, Steve Tikolo (captain), Tanmay Mishra, Collins Obuya, Thomas Odoyo, Jimmy Kamande, Lameck Onyango, Peter Ongondo, Hiren Varaiya.