Leicester have one point from their opening six games and, despite taking the lead inside a minute, were outplayed in a performance that will add to the substantial pressure on manager Brendan Rodgers after a summer of discontent at the club.
"The best team won and that's the reality of it," Rodgers told Sky Sports. "We got off to a great start to the game, but made mistakes to allow them back into it.
"With the ball, we gave it away so cheaply. A team in confidence can see it through, but the guys are suffering with that at the moment.
"They gave everything to the fight, but the mix of quality, [lack of] confidence and mistakes... we're just suffering."
Kelechi Iheanacho put Leicester in front and Patson Daka drew them level at 2-2 before half time, but an own goal from defender Luke Thomas and strikes from Moises Caicedo, Leandro Trossard and Mac Allister, one from the penalty spot and the other a superb free kick, sealed victory for the home side.
Mac Allister was also denied what would have been a contender for goal of the season when his thunderous strike from 30 yards was ruled out after a Video Assistant Referee (VAR) check that lasted almost five minutes. Enock Mwepu was adjudged to have been in an offside position and interfered with play in the build-up.
The scoreline flattered the visitors, who looked tentative in their defending and have conceded 16 goals in six league games.
Brighton, who climbed into the top four, travel to south coast rivals Bournemouth on Saturday while Leicester host fellow strugglers Aston Villa in what is shaping up to be a must-win game for Rodgers.
"It was a great performance and an amazing win," Brighton manager Graham Potter said.
"The players were incredible to recover like we did and we were the better team. The second-half performance was fantastic.
"The boys stuck to the task and played well over the game. I'm a little disappointed with the goals we conceded, but I'm not going to be picky when we scored five."
Information from Reuters contributed to this report.