Kenyan batsman Steve Tikolo ended up on the losing side playing his last ODI.
Kolkata: Craig Ervine provided an important thrust to the innings as Zimbabwe set Kenya a big target and then completed a 161-run rout on Sunday in the last Group A match of the World Cup.
Ervine's stroke-filled 66 stood out in a batting performance that helped Zimbabwe score an imposing 308 for six after electing to bat in the inconsequential match.
In reply, Kenya was all out for 147 in 36 overs in the face of some tight bowling by the spinners.
Zimbabwe finished with two wins after having beaten Canada earlier in the league, while Kenya remained without a win.
Kenya was led by veteran allrounder Steve Tikolo in his last match after regular captain Jimmy Kamande was ruled out due to a knee injury.
Kenya's batting succumbed in the face of Zimbabwe's first 300-plus total in the tournament.
Ervine provided the impetus amid a strong middle-order batting performance, striking a brisk 66 and adding 105 runs for the fifth wicket with Elton Chigumbura, who made 38.
Ervine struck nine fours and a six during his fluent 54-ball knock, during which he often worked the ball cleverly off his legs. He was out in the 48th over when he played on a delivery from pace bowler Elijah Otieno.
But the Kenyans got no respite as Prosper Utseya struck 19 off just six balls, including a six and three boundaries off the first four deliveries off the last over of the innings bowled by Otieno.
Zimbabwe had earlier made up for two early dismissals as Tatenda Taibu and Vusi Sibanda added 110 for the third wicket in just under 20 overs.
The partnership was broken due to a mix up that saw both batsmen at the same end. Sibanda had to go back after an entertaining 57-ball 61 in which he hit seven fours and a six to Tikolo that had taken him to his 13th half-century.
Taibu struck 53 off 74 balls, completing his 18th half-century as well as 3,000 runs in limited-overs internationals with a well-timed four to the point boundary. But he was out soon after as he tried one reverse-sweep too many against legspinner James Ngoche and was trapped lbw.
The Kenyan batting lineup struggled from the start.
After pace bowler Chris Mpofu provided the initial breakthrough by trapping David Obuya lbw, left-arm spinner Ray Price showed his expertise with the new ball.
He removed Tikolo and well-set opener Alex Obanda, both lbw. Collins Obuya was run out and Utseya removed Tanmay Mishra as half the Kenyan side was dismissed by the 12th over.
The game meandered on from then with Kenya only ensuring there were no embarrassment, Nehemieh Odhiambo making an unbeaten 44.