Half-centuries from Hugh Morris and Matthew Maynard put Glamorgan in sight of their target, but the England seamer turned the game. While Frank Griffith removed Viv Richards, Cork bowled Maynard for 69.
Glamorgan, now batting in driving rain, finally needed 11 off the last over. Griffith, though, had Robert Croft taken at gully and Colin Metson was caught by Cork going for the winning hit.
Trevor Ward, as stylish as they come but due for a few, came up with a Sunday-best 99 at Canterbury in seeing Kent home to their second successive victory in the league.
Ward scored his runs off 114 balls to set up the 66-run win, taking eight fours and two sixes off the Warwickshire attack before driving Allan Donald, who later added a dislocated finger to a dodgy hamstring, to short extra with his century in sight.
Mark Ramprakash, on England stand-by for Neil Fairbrother in Wednesday's Texaco Trophy match with Australia, scored 88 as the champions Middlesex beat Nottinghamshire by five runs at Lord's.Reuse content