It was Sussex’s other overseas player, Ross Taylor, who set up the win with a measured 62 off 50 balls. Sussex were struggling on 68 for 4 after 12 overs in their response when Taylor was joined by Chris Jordan in a match-winning stand of 61 from 39 balls.
Taylor struck off-spinner James Tredwell for 16 off three balls in the 16th over to tilt the contest Sussex’s way and although both he and Jordan (16) fell to catches in the deep off Mitch Claydon in the penultimate over, Wiese held his nerve to secure a third win out of four in the South Group for his side.
Claydon took 3 for 25, having earlier bowled Ben Brown (26) while Matt Coles also impressed, finishing with 1 for 17 and claiming the key early scalp of Sussex skipper Luke Wright, who was caught at deep square leg for three.
Kent had been bowled out for 140 off the final ball of their innings, having been put in, after some impressive work from Sussex’s seamers on a slow pitch.
England international Jordan led the way with 3 for 18. In his first spell he removed Daniel Bell-Drummond (17) with a slower ball and returned to the attack to have Alex Blake (3) caught at cover and Darren Stevens (17) at mid-wicket.
Jordan was well backed up by left-armer Tymal Mills, whose searing pace made it tough for the Kent batsmen. Mills yorked Coles and then removed Tredwell and Griffiths in his final over to finish with 3 for 15 while Wiese took 2 for 33 including Kent captain Sam Northeast, who returned to form with 53 off 33 balls which included two fours and four sixes, all struck in the area between long on and mid-wicket before he mis-timed a leg-side pull allowing Wiese to take a simple return catch.
Sussex’s seamers were well supported by leg-spinner Will Beer, who had the dangerous Sam Billings (10) lbw sweeping as Kent’s innings tailed off alarmingly, with the last five wickets falling for nine runs.
Man of the match Ross Taylor, who made 62, said: “Chasing 140, you normally think you are going to win but you have to give Kent credit, they came at us hard.
“Mitch Claydon brought them back into it in the 19th over with those two wickets but David Wiese is an experienced international cricketer and he didn’t freeze in the final over and got us over the line.
“It was a bit too close for comfort but the pitch did help the bowlers a bit so it was nice to get us over the line. I just thought if I could bat for as many over as possible that we’d get close and fortunately that proved to be the case.”