The home side raced into a two-goal lead before one of Micky Adams recent signings, Ricardo Scimeca, pulled a goal back for the Foxes with a superb 25-yard free-kick.
James Scowcroft levelled matters on the hour but Brighton sealed victory five minutes from time through Nathan Jones.
Leicester: Walker (Coyne 45), Sinclair (Impey 45), Thatcher, Hignett, Izzet, Gillespie (Brooker 45), Scowcroft, Deane (Stewart 45), Howey (Rogers 45), Elliott, Scimeca (Nalis 45).