The Foxes took the lead within the first two minutes as Riyad Mahrez weaved his way into the box before unleashing a low effort on goal, which Mathew Ryan parried into the path of Shinji Okazaki for a simple tap-in.
Brighton began showing more ambition as the first half wore on, but Leicester were unlucky not to score again 18 minutes in through Jamie Vardy, who was well positioned in front of goal after receiving a low cross from Okazaki but scuffed two efforts in quick succession.
Aside from a 24th-minute volley from Glenn Murray that hit the back of the net but was rightly ruled offside, Leicester were dominant in the first half and would have been disappointed to go in at the break just one goal up.
It did not take long for the Foxes to rectify this after the restart, however, as 54 minutes into the game, Harry Maguire rose at the back post to head in a Mahrez corner and all but kill off the Seagulls' resistance.
Despite being able to see out the game without too much effort, Leicester's afternoon was soured when Vardy went down after contesting a 50-50 ball with Ryan and, when substituted, hobbled off the pitch.