Sussex resumed on 113-3 but in twenty one overs, Ant Botha had taken five wickets and Sussex were all out for 172.
Botha removed Kirtley, Hopkinson, Joyce, Chawler and Rayner to record figures of 5-51. Boyd Rankine took two wickets and gave Warwicks a victory by an innings and two runs.
Tomorrow, Warwicks are in Pro40 action with a trip to Canterbury to play Kent.