Sussex are facing Vitality Blast elimination after losing a low-scoring thriller in Cardiff.
Glamorgan, with six wickets down, plundered 19 runs off the 19th over to settle an increasingly tense run chase, having been set 150 to win.
It was Sharks' fifth successive defeat.
They must now win their last four South Group games to have any chance of going through to the quarter-finals.
That starts with the visit of Chris Jordan and leaders Surrey to Hove on Thursday.
Sussex never really going in their innings although Luke Wright, limping due to a foot injury, made 46 off 35 balls, his best score yet in this season’s Blast.
A flurry of wickets late in the Glamorgan reply left them needing 18 to win off two overs.
But a six by Dan Douthwaite off Steven Finn helped them take 13 off the first five balls of the 19th.
James Weighell, facing his first ball, then added a huge six to finish the job.
Colin Ingram, dropped by Delray Rawlins at slip on nought, was top scorer in the match with 57 off 43 balls.
Sussex lost Mohammad Rizwan early as he looked to play his favourite pull shot and was caught on the deep square leg boundary.
They were 12-2 in the third over when Michael Neser bowled Ali Orr, looking to run the ball down to third man.
Sussex were a modest 38-2 off the powerplay but Wright plundered three fours through the off-side off Weighell in the seventh over.
Tom Alsop was badly dropped on 19 at mid-wicket by Eddie Byrom but Sharks never really got away.
Wright was caught for 46 at long-on as Neser ran in and held the chance low down.
Sharks lost three wickets for 17 as Ravi Bopara and Alsop, whose 34 came off 28 balls, were both caught in the deep looking to accelerate.
That sort of ambition also saw Harrison Ward stumped as he went down the pitch to Andrew Salter, who he had just smashed for six.
Rashid Khan was yorked but Sussex got some of the late impetus they needed from Rawlins.
He straight drove two sixes and a four as the 19th over, bowled by Douthwaite, went for 21.
Rawlins (27 off 16) was out lbw to a Neser full toss from the first delivery of the 20th as Sussex closed on 149-8..
They had the early breakthrough they needed when David Lloyd drove Finn to Khan at mid-off at the end of the second over.
But it should have even better.
Ingram was dropped on nought by the diving Rawlins at slip off Tymal Mills, with the loose ball then rolling almost apologetically over the rope for four.
Khan was introduced for the fifth over and went for 12 as the reprieved Ingram cut the last two balls to the rope across a rapid outfield.
The hosts were 51-1 at the end of the powerplay.
Sam Northeast and Ingram added 86 for the second wicket in just short of 11 overs.
Progress was slowed a little after Northeast (35 off 32) perished to a catch on the boundary by Henry Crocombe off Mills.
Ingram went after Rawlins as the hosts took 13 to leave 26 to get off four overs.
But Kiran Carlson scooped a drive to the hands of Bopara at extra cover off Mills.
Byrom was caught by Alsop at deep backward point off the next ball.
Douthwaite hit a six later in the over but that was the only scoring shot, leaving 20 required off 18 balls.
Over No.18, delivered by Bopara, went for just two runs – and brought two wickets.
Ingram thought he had clubbed the skipper for six over long-off but Khan brilliantly spooned the ball up as he went over the rope, then recovered to complete the catch.
Alex Horton edged behind to Rizwan off the final ball of the over and Glamorgan had lost four for eight.
But Bopara was not to get the chance to deliver the 20th over as Glamorgan settled matters.