Northamptonshire, looking to make their fourth successive appearance in the last four, needed 85 more off 20 overs to win the unfinished tie. When play resumed, though, Sussex romped away to victory by a comfortable 40 runs after taking the remaining seven wickets for 43 in 14 overs.
Mal Loye fell to the 10th ball of the morning and the big-hitting Kevin Curran also made a rapid departure. Nigel Felton, unbeaten on 40 at the start, meanwhile was caught at long on after making a painstaking half- century. By then, Northamptonshire were well on their way to being dismissed for 190 in 55.2 overs. The Sussex all-rounder Franklyn Stephenson took the man of the match award with figures of 2 for 25 from his 11 overs.
'Our game plan was to keep pressure on Felton by stopping him nudging and deflecting the runs he was getting early in his innings,' Alan Wells, the Sussex captain, said. 'The pitch was getting slower and it was getting harder to score in that way. We gave nothing away and bowled very tightly. We reached the semi-final in 1986 and went on to win the trophy. Hopefully this is an omen.'
Warwickshire were also celebrating at Headingley after Yorkshire slipped away to a 21-run defeat despite a sixth-wicket stand of 105 in 24 overs between Richard Blakey and Craig White. Resuming at 69 for 5, Yorkshire failed to recover from their perilous overnight position, though Blakey, 75, and White, 46, recorded their best scores in the competition.
White survived until the 53rd over. Allan Donald, in his last appearance for Warwickshire, then bowled Peter Hartley. Yorkshire needed 48 from the last four overs, but their hopes disappeared when Blakey fell to Paul Smith, who finished with 4 for 37.
There is still the prospect of a Lord's farewell for Viv Richards, Glamorgan finishing off Worcestershire at Swansea by 104 runs with 9.1 overs remaining to progress to their first 60-over semi-final for 16 years.
Worcestershire, who started on 40 for 2 from 23 overs, were in need of major contributions from Graeme Hick and Damian D'Oliveira with the asking rate hovering around 6.5 runs an over. Hick, however, had added only eight before he pulled Adrian Dale to midwicket. D'Oliveira hit 24 in 19 balls but then fell attempting to smash Steve Barwick over mid-on, where Roland Lefebvre was again lurking. That left Worcestershire seeking 179 in 29 overs, a task that proved beyond them on this occasion.