They were restricted to 166 for 8 in their 40 overs after Mike Watkinson chose to bat first, with Ian Salisbury taking 2 for 30 and Paul Jarvis 2 for 17 for the visitors. Sussex collapsed to 144 all out in reply as Wasim Akram took 4 for 16 in seven overs.
Aravinda de Silva, the Sri Lankan Test player, kept Kent's title hopes alive, hitting a superb 124 - his highest score in one-day cricket for the county - as they recorded their eighth win in the competition, beating Surrey by 55 runs at Canterbury.
De Silva shared a record second-wicket stand of 241 with Trevor Ward, who made 123 in just 34 overs.
A brilliant unbeaten century from Graeme Hick enabled Worcestershire to maintain their challenge for the title as they crushed Yorkshire by 33 runs at Scarborough.
The England batsman reached three figures in the competition for the second time this season. His 113 came from only 83 balls as he hit two sixes and 12 fours in Worcestershire's innings of 251 for 4.
Yorkshire, who were never in touch with the necessary run-rate, could not recover from a poor start, in the course of which they slumped to 45 for 3. Michael Bevan provided the backbone for the innings, scoring 101 from 92 balls as Yorkshire reached 218 for 9 in their 40 overs.Reuse content