Kent 173 for 7 (Stevens 67*) beat Sussex 164 for 6 (Machan 67) by nine runs
Kent edged victory by nine runs in the basement battle against Sussex watched by a near 4,000 crowd at Canterbury.
The visitors' challenge faded when Scott Styris was caught on the deep-midwicket boundary from the fourth ball of the final over, having hit the previous two balls for four and six.
New Zealand international big-hitter Styris had the home fans on edge as Mitchell Claydon made a bad start to the task of preventing Sussex from scoring 23 from the final over in reply to Kent's 20-over total of 173 for 3. But then Styris, attempting another clubbing legside blow, holed out to Brendan Nash at deepmidwicket.
Despite bowling a wide to new batsman Will Beer from his next ball, Claydon held his nerve to allow just a single and a leg bye from the last two balls of the contest to close out Sussex on 164 for 6.
It is only Kent's second win of the group stage, but at least they now go above Sussex - who are anchored at the bottom of the South group table with just one win from nine games. Kent still have three matches left.
In the end, Kent were indebted to a late assault by Darren Stevens - who finished on 67 not out - and a far faster start to their innings than Sussex. Stevens faced only 44 balls in all, striking four sixes and three fours, and took 18 runs from the last six balls of the Kent innings in a merciless attack on Lewis Hatchett.
Kent scored 70 for 2 from their first six Powerplay overs, but Sussex managed only 39 for 1 from theirs. Although Matt Machan hit 66 from 48 balls, with two sixes and six fours, and added 68 for the third wicket with Chris Nash, who made 31 from 24 balls, they were always struggling to keep up with the required rate of 108 from the second 10 overs.
Earlier, Nash's clever four overs of offspin had brought Sussex back into the game. He went for just 15 runs but Styris, mysteriously overlooked for the final over, conceded just 13 runs from his three overs. That final Hatchett over was to cost Sussex dear.
The Kent innings was given a flying start by the youthful opening pair of Fabian Cowdrey - son of Chris and grandson of Colin - and Sam Billings, who put on 60 in 5.2 overs before Billings was bowled for a 14-ball 24, swinging at Chris Liddle.
Cowdrey, 20, got things moving by hitting Mike Yardy for successive fours from the first three balls of the third over and Billings joined in by pulling a full toss for six from the fifth ball of the same over.
Billings, 22, then drove fours through extra cover off Liddle before Cowdrey swung Hatchett over midwicket for six to bring up Kent's 50 and then earned four more from a ramp shot to fine leg off the same bowler. There was a further six from Cowdrey, driven straight off Liddle, before he fell for a brilliant 40 off just 21 balls when, deceived by a slower ball from left-arm paceman Liddle, he mishit to cover.
Nash, in at No. 3, could not get going and made only 15 from a third wicket stand of 52 in 10 overs with Stevens before the returning Liddle bowled him. But Stevens,who had already hit Yardy over the midwicket boundary and driven leg-spinner Beer straight and to wide long-on for successive sixes, then provided the explosive finish in a final over which cost Sussex 20 runs, with Hatchett starting it with a high full toss that went down in the book as two no balls.
Veteran all-rounder Stevens then sprinted for three twos before flipping another full toss for four, hitting another two into the legside and then, from the last ball of the innings, carving a short ball over cover for six.