Surrey, whose innings was twice interrupted by rain, scored 251-7 in 41 overs thanks to the returning Jason Roy's 44 and Ben Foakes' 82 not out.
Kent, set a revised target of 249, lost regular wickets in the chase.
England's Sam Billings struck 69 off 65 balls, but once he fell to Sam Curran, Kent's innings folded to 204 all out.
Surrey will need to win their final two group games against Hampshire and Gloucestershire to stand a realistic chance of going through, while Kent have only won one of their six matches.
England one-day opener Roy, playing his first game of the season for Surrey, got the innings off to a flying start with a run-a-ball knock before he was caught at deep-square leg off seamer Ivan Thomas.
But Foakes continued his fine form in the competition, reaching his fourth half-century in five innings, to give Surrey a defendable total.
Only Billings, also making his first county appearance of the season, could find any momentum for Kent in the chase, striking three sixes, but his dismissal by Sam Curran sparked the loss of the visitors' last four wickets in 18 balls.
Surrey boosted their hopes of qualifying from the One-Day Cup South Group with a 44-run victory over eliminated Kent at The Oval.