Ross Taylor hit 85 but was struck down with a hamstring strain in New Zealand's 331 for seven, the highest one-day international score here, although a crowd of around only 4,500 was in the 20,000-capacity Beausejour Cricket Ground to see it.
Kenya never got going in their rain-interrupted reply, slumping to 29 for four before being bowled out for 183 with four balls left.
Lou Vincent was instrumental in two of three run outs while Michael Mason, Daniel Vettori and James Franklin all took two wickets.
Ravindu Shah offered some resistance, stroking a 89-ball 71 before he was superbly caught-and-bowled by Vettori a ball after launching him for six. Thomas Odoyo was the other notable contributor with well struck 42 off 67 balls studded with four boundaries and a six over long-on off Vettori.
The result also meant Canada, who play the Kiwis on Thursday, were definitely eliminated. Kenya face England in the last group game on Saturday to determine the other Super Eight qualifier.
New Zealand were put into bat but their innings was packed with good scores as Kenya's slower bowlers failed to show the form that took them to a seven-wicket win over Canada in their first match.
Craig McMillan struck five sixes in his 71 while Scott Styris, who hammered 87 not out in the win over England on Friday, was dropped twice but made 63 off 62 balls.
Taylor played a patient knock before pulling up in the 32nd over and calling for a runner. He only lasted two more overs before being caught and bowled by Kenya captain Steve Tikolo, two balls after smashing him for six.
The 23-year-old was fortunate to reach his third one-day fifty after Tanmay Mishra failed to cling on to a difficult chance in front of square in the fourth over. Taylor also survived a close run-out with Mishra again the fielder.
The innings had started poorly with opener Lou Vincent out for a second successive nought in the fourth ball of the day but captain Stephen Fleming steadied matters before running himself out on 60.
The Black Caps dispensed with their twin spin bowling attack, Jeetan Patel making way for paceman Mason.
Kenya also made one change with Lameck Onyango coming in for bowler Nehemiah Odhiambo.