Jamie Vardy ended a run of five Premier League home appearances without a goal, since 1 December
New Leicester manager Brendan Rodgers watched from the stands as the Foxes beat struggling Brighton in the Premier League.
Rodgers was confirmed as boss an hour before kick-off, although Mike Stowell and Adam Sadler took caretaker charge after the sacking of Claude Puel on Sunday.
Demarai Gray opened the scoring as he ran onto Youri Tielemans' pass to smash home.
Glenn Murray missed a glorious chance to equalise, when he blazed the ball over from six yards out.
Jamie Vardy doubled Leicester's lead from James Maddison's pass, but Davy Propper gave Brighton hope three minutes later with a crisp low drive.
The Seagulls, who have yet to win a Premier League game in 2019, could not find an equaliser and remain three points above the relegation zone.
Signs of encouragement for RodgersBrendan Rodgers acknowledges the crowd at King Power Stadium before kick-off
Puel was sacked on Sunday after a 4-1 defeat by Crystal Palace, a sixth loss in seven games. Leicester players were reported not to be happy with the Frenchman's methods, while Foxes fans never really warmed to him.
But they instantly seem to have taken to Rodgers - who has led Celtic to consecutive Scottish trebles and guided Liverpool to the brink of the 2013-14 Premier League title.
The Northern Irishman, who takes charge for the first time at Watford on Sunday, received a standing ovation from the fans when he was introduced before kick-off.
As a manager who plays an attractive brand of football and gives youth a chance, he will like what he saw going forward.
Harvey Barnes was excellent on the left wing, causing Brighton problems throughout, with Tielemans pulling the strings in midfield and Gray on the scoresheet. Maddison looked back to his playmaking best after a reduced impact in recent weeks, while Ben Chilwell offered attacking options from left-back. All those players are 22 or younger.
The opening goal involved three of them as Barnes won the ball on the halfway line before finding Tielemans, whose perfectly weighted pass was finished by Gray, who timed his run well.
Gray almost added a second moments later was but denied by a good low Mat Ryan save.
The second goal saw Gray and Maddison link up before Vardy ran through to finish for his second goal in three games.
They conceded soon after, but showed good defensive resolve to see the game through and pick up their first home win since beating Manchester City on 26 December.
Rodgers came into the changing room after the game to tell the players his plans for the future and that he was proud of them, caretaker boss Stowell said.
Leicester 2-1 Brighton: Brendan Rodgers appointment gave players a boost - Mike StowellMixed performance for BrightonGlenn Murray showed uncharacteristic lack of composure in front of goal
Brighton played really well in parts, but their worrying slide continues. The last time they won in the Premier League, on 29 December against Everton, they were 11 points clear of the bottom three and looked in no danger.
But their only three wins since then have all been in the FA Cup on their run to the quarter-finals. Two points from their past seven games have left them in real relegation trouble.
They created plenty of chances at Leicester, with 15 shots in total, and Murray was guilty of their two worst misses.
The 35-year-old, who has scored 106 goals in two spells for Brighton, hopelessly fired over after Pascal Gross' backheel had picked him out in space. The playmaker injured himself in picking out Murray and had to be replaced.
Murray replaced his boots immediately after missing that chance but his new footwear also let him down two minutes from the end as he slammed a volley into the side-netting.
Anthony Knockaert forced a good save from Kasper Schmeichel in the first half while most of their other chances came from corners, with Shane Duffy and Lewis Dunk missing several opportunities each.
They did not defend poorly, with both of Leicester's goals coming from pacy forwards chasing through-balls, but Chris Hughton knows his team need to start taking their chances and conceding fewer goals if they do not want to drop back into the Championship.
Man of the match - Harvey Barnes (Leicester)Harvey Barnes had an electric performance on the wing. He could be an England prospect if he works on his finishing - none of his seven shots were on targetMatch stats - Gray's best Premier League season
Brighton (P7 D2 L5) are the only side in the top four tiers of English Football still to win a league game in 2019.Leicester are unbeaten in 15 home matches played on Tuesday (W11 D4) since losing 4-2 to Chelsea in the League Cup third round in September 2016.Brighton have conceded two or more goals in five consecutive away league games - the Seagulls last went on a longer such run between December 2005 and February 2006 whilst in the Championship (seven games).Leicester are unbeaten in their past 33 Premier League games at the King Power Stadium in which they have scored the opening goal (W29 D4), since a 5-2 defeat against Arsenal in September 2015.Maddison is the first English midfielder to be involved in 10 goals in the Premier League this season (five goals, five assists).Demarai Gray's opener after nine minutes and 22 seconds was Leicester's fastest league goal of this campaign - he has now scored four goals in the 2018-19 Premier League, his best return in a league campaign since six in the 2014-15 Championship season with Birmingham.Jamie Vardy has scored in his past three Premier League appearances for Leicester against Brighton.What's next?
Rodgers takes Leicester to Watford, his first managerial club, on Sunday (12:00 GMT). Brighton are at home to bottom side Huddersfield Town on Saturday (15:00 GMT).