Goals in the opening five minutes by Patrick McCarthy and Iain Hume earned the Foxes a third straight victory under caretaker boss Rob Kelly.
Alex Frutos pulled a goal back for Brighton in the second half, but they finished with 10 men, Dean Hammond seeing red a minute from the end for a second bookable offence.
McCarthy, Leicester's captain in the absence in the absence of Danny Giatto, gave his side a dream start in the fourth minute. A corner by Johannes Gudjonsson found the centre-half unmarked at the far post, and he volleyed in from close range.
Worse followed for Brighton a minute later as a mistake by Adam El-Abd allowed Gudjonsson to release Hume with a pass through the middle. The Canadian international calmly rounded Brighton keeper Wayne Henderson to double Leicester's lead.
A shell-shocked Brighton rarely threatened to get into the game in the opening 45 minutes, but they were thrown a life-line 11 minutes into the re-start by Rab Douglas. The Leicester keeper made a mess of a punch from Hammond's high cross, and Frutos pounced to rifle in their third goal of the season.
Brighton came close to equalising on several occasions. Joe Gatting, an18- year-old striker making his full debut, fired over from the edge of the area after captain Guy Butters had a shot blocked.
French winger Sebastien Carole then wriggled away from two challenges to test Douglas with an angled drive which the keeper pushed for a corner.
Brighton's Gary Hart stabbed straight at Douglas in the 73rd minute when a shot from team-mate Paul McShane landed at his feet. That proved to be the home team's last opportunity and their misery was completed by Hammond's dismissal. The central midfielder, booked in the first half for a foul on Gudjonsson, received his marching orders when he clipped the same player from behind.