Defender Harry Maguire also netted his first goal for the Foxes mid-way through the second-half to secure the points for the hosts in their first home match of the season.
Going into the game at the King Power Stadium, Leicester boss Craig Shakespeare named an unchanged team for the clash with the newly-promoted Seagulls. Leonardo Ulloa though replaced Kelechi Iheanacho on the substitutes bench with the Nigerian forward suffering from a toe injury.
Elsewhere, the Seagulls made two changes from the 2-0 loss to Manchester City last time out. Glenn Murray and Jamie Murphy were named in place of Tomer Hemed and Izzy Brown.
Lightening start for the Foxes
Despite the alterations for the visitors, it did not take long for Leicester to seize the initiative. Seizing the ball from a Brighton attack, Riyad Mahrez, who was a shining light all afternoon, jinked into the penalty area on the right-wing. Cutting the ball onto his left foot, the Algerian produced a testing low drive.
The shot was saved by Mathew Ryan in the Brighton net but his parry fell to Japanese forward Shinji Okazaki who rolled the ball into the empty net from only a few yards out to give the Foxes the lead, also continuing his good form having scored against Arsenal last weekend.
Shakespeare's men could have even doubled their advantage had Jamie Vardy not miscued his effort following an excellent cut-back from Wilfred N'didi.
Okazaki then had another chance as he latched onto a Vardy cross but his shot flew just wide of the goal. The Foxes were comfortably on top and went into half-time deservedly leading.
Limited chances for Seagulls
Going into the second period, Brighton needed to push forward more in an effort to get back into the game. However, that only served to make the Foxes more comfortable and it was not long before they netted again.
Riyad Mahrez whipped in an excellent corner kick and home debutant Harry Maguire leapt highest and found the net with an excellent header.
Following Leicester's second goal, Chris Hughton's men finally found a foothold in the game and started to enjoy a few chances. Glenn Murray was unlucky to put wide from inside the penalty area before substitute Tomer Hemed unleashed a shot from distance that was well-saved by Kasper Schmeichel.
The red-hot Mahrez then nearly notched a goal of his own as he met a Marc Albrighton cross. Lewis Dunk though was on hand to deflect the winger's shot away from goal.
The only concern for Craig Shakespeare following the victory would be an injury sustained to Jamie Vardy. The England striker appeared to have picked up an ankle knock in the closing stages of the game.
Despite that, the Foxes' strode home to secure their first win of the season whilst Brighton have suffered consecutive 2-0 defeats. Focus will now switch to the EFL Cup as Leicester and Brighton face Sheffield United and Barnet respectively on Tuesday evening.