The Sharks closed on 134 for six, Luke Wright's 39 and Delray Rawlins’ 33 steering them into the last eight with 2.5 overs to spare.
Earlier Ravi Bopara took three for 15 and David Wiese two for 16 as a Kent side with 15 first-teamers still isolating struggled 130 for seven, Calum MacLeod their top scorer with 31.
Kent had already ensured top spot in the South Group and will play their quarter-final at the St Lawrence despite tonight’s defeat, while Sussex are likely to be away, pending the outcome of the Somerset v Gloucestershire game.
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Kent won the toss and chose to bat, but Wiese quickly removed the openers, getting George Munsey caught by Oliver Carter for 11. Zak Crawley was given a life when Harrison Ward fell over while attempting to catch him at deep point, but Wiese then deceived him with a slower ball, which he chipped to Ollie Robinson at mid on for 19.
Will Beer caught and bowled Heino Kuhn for four with his first ball, before Harry Finch and MacLeod partially rebuilt the innings with a stand of 44.
Finch, however, fell for 30, caught by Ollie Robinson off Bopara and when MacLeod was lbw to Rashid Khan, Kent were 101 for five.
It was left to the lower order to nudge the score towards respectability. Dan Lincoln was caught by Wiese for 10 and the same combination removed Harry Podmore for 0, leaving Marcus O’Riordan and Safyaan Sharif unbeaten on 13 and seven.
The target looked low and although Elliot Hooper bowled Phil Salt for a duck with the third ball of Sussex’s innings, Wright and Bopara put on 61 for the next wicket. There was a wobble when the former holed out to O’Riordan and was caught by Munsey for 39, and Bopara was out in the same over for 19, caught by Matt Quinn.
However, Crawley stumbled when well-placed to catch Rawlins and by the time Wiese was caught by Kuhn off Podmore for 21, the run rate was down to 2.8.
Just two were needed when Kuhn made a diving catch off Podmore to dismiss Ward for 8 and Rawlins skied the next ball to O’Riordan, but Khan hit the winning runs with a four through cow corner.
Report by Fred Atkins