Andy King stabbed home the only goal of the game in the 10th minute, but they had goalkeeper Kasper Schmeichel to thank for preserving the points as he denied Ashley Barnes from the penalty spot.
Leicester, who had moved to the summit on goal difference following a 1-1 draw at Birmingham on Saturday, named an unchanged starting line-up.
Brighton, who went into the game on the back of a four-match winless run, made two changes from the side beaten at home by Middlesbrough last weekend.
Will Buckley replaced David Lopez and Gary Dicker came in for Dean Hammond.
Leicester started brightly, with Martyn Waghorn's skidding 30-yard free-kick forcing goalkeeper Tomasz Kuszczak into an early save.
The Foxes took the lead after a spell of early pressure. Some fine work from David Nugent down the left saw him beat Liam Bridcutt and cut inside before laying the ball to King.
King's initial shot was blocked by Kuszczak but the ball rebounded kindly to him and the midfielder stabbed home from close in.
The home side were rampant and almost added a second shortly afterwards when Ritchie De Laet broke away and crossed into the path of Waghorn but he could not keep his shot down.
Brighton responded through a Bridcutt free-kick which was pushed wide by Schmeichel, with Barnes heading over from the resulting corner.
But Leicester were quickly back on the attack as Anthony Knockaert neatly controlled a pass from Waghorn and drove in a shot which was palmed away by the keeper.
The Seagulls, who had scored just one goal in their previous four matches, were dominating possession as the first half drew to a close but struggled for an end product as Buckley's volley flew well wide.
Kuszczak pulled off a superb save to keep out Nugent's curling effort at the start of the second half, but from the quick break, Brighton were awarded a penalty.
Zak Whitbread was adjudged to have fouled Buckley, but Brighton's profligacy continued as Barnes' penalty was saved low by Schmeichel.
De Laet left the action through injury shortly afterwards with Liam Moore coming on, while Nugent made way for Jamie Vardy moments later.
And after Vardy had glanced a header wide from Lloyd Dyer's cross, Foxes manager Nigel Pearson made his third change, with Ben Marshall replacing Waghorn.
Craig Mackail-Smith, who had been quiet, was inches away from connecting with a cross from Bruno Saltor, while at the other end Marshall had Kuszczak scrambling to keep out a low drive.
Barnes had the chance to make amends for his penalty miss at the death but he fired wide and the Foxes held on.