In a match reduced to 35 overs a side because of wet conditions, the CI were all out for 128 in 31.5 overs chasing 175 for victory.
The CI were looking good for a while before eventually collapsing.
They lost three middle order batsmen in a four run period and then their hopes of reaching the last eight disappeared after losing their last four wickets for just four runs.
Jersey’s Dave Gorman top-scored for the CI with 38 runs following four boundaries facing 68 deliveries in a 62-minute stay at the crease.
Earlier Mike Coward took three Kent wickets for 37 runs in a seven-over spell.
