Drizzle just before play was due to start at 11:00 [BST] meant the action was delayed by 10 minutes and resulted in an over being docked off each innings.
Perhaps buoyed by successfully chasing down 294 and 314 in their past two group matches, Kent chose to stick Surrey in after winning the toss but could not take advantage of any early moisture as Patel and Sibley got the home side off to a confident start.
Left-hander Patel, in particular, looked in superb touch, lashing 13 fours and one six in collecting his fourth half-century of the competition off 54 balls as the openers put on 116.
He looked well set to convert that into a hundred but mis-hit a lofted square drive off the left-arm spin of Denly and was caught in the deep, 27 short of three figures.
That slowed their momentum, with 10 overs passing without another boundary, as Sibley was drawn into grazing a tempting leg-spinner from Matt Parkinson to wicketkeeper Chris Benjamin four balls after reaching his 50.
But skipper Burns launched a savage counter-attack, with 26 of his 33 runs coming in boundaries before he slapped Grant Stewart to extra cover.
Sykes then emulated his captain with three Row-Z sixes before a slower ball from Singh induced a skied catch to deep mid-wicket.
Josh Blake, with a measured 27-ball 32, did his best to get Surrey to 300 but when he perished to the excellent Milnes the home side’s hopes of that mark fell away as they were bowled out 14 runs short.
In reply, Kent struggled to get going, managing only 33 off their opening powerplay as Ben Dawkins was brilliantly caught behind the stumps one-handed by Burns for nine as he drove on the up off Lawes.
Patel picked up the key wicket of in-form skipper Daniel Bell-Drummond for 27, as he, Sam Northeast (24) and big-hitting Chris Benjamin (0) all perished within eight overs.
Denly and Singh’s entertaining effort prevented Kent from collapsing in a heap but when Denly feathered a ramp shot to Burns off Lawes, the writing was inked on the wall.
Surrey’s victory means they trail the Foxes on net run rate going into the final two group games, with the side finishing top securing a home semi-final.
In Wednesday’s other game in the One-Day Cup in Group B, last year’s runners up Hampshire kept their hopes of reaching the knockout stages intact with a 90-run win over Glamorgan in Southampton.
