Despite Kabir Ali's efforts to conjure a victory that would have been dramatic even by the standards of this competition, Glamorgan completed their fourth win from five matches to earn a home tie in Monday's Twenty20 Cup quarter-finals.
Chasing 141 to win in a contest reduced to 16 overs per side, Worcestershire were threatening to record the lowest all-out total so far as they slumped to 46 for 8 at the halfway point.
But an extraordinary display of devil-may-care hitting by Kabir, whose 28-ball assault included four sixes, made Glamorgan sweat before Dean Cosker's safe hands held a steepling catch to dismiss him one short of a half-century, confirming the Welsh side's victory by 20 runs with 11 balls to spare.
Ian Thomas hit five boundaries to reach 23 from 12 balls before skying Andy Bichel to cover. After a break for rain, Michael Powell played on to Nadeem Malik but Matthew Maynard's 44 from 34 balls - terminated by a brilliant one-handed catch by Graeme Hick at deep backward square - put them back on course.
Worcestershire's pursuit of their target fell into disarray when three wickets fell in the third over, Alex Wharf bowling Gareth Batty and inducing Ben Smith to glove a catch to square leg, with Vikram Solanki unluckily run out, backing up. Only Kabir's explosive intervention prevented an embarrassing defeat for the home side in front of another sell-out crowd.