Andy King had reduced the score to 2-1 for the Foxes in the second half but a penalty from Barnes put the result to bed as Leicester slipped to their second successive defeat in the Sky Bet Championship.
The sit third in the table, one point behind leaders Burnley, while Brighton move within three points of the play-of places.
The hosts were forced into a late change when goalkeeper Casper Ankergren injured himself in the warm-up and giant Slovakian Peter Brezovan came in for his first appearance of the season.
Brezovan was called upon to make an important save in only the fourth minute by parrying a goal-bound shot from Danny Drinkwater.
The Seagulls then stunned their opponents by taking a ninth-minute lead when Barnes notched his fourth goal in five games. The striker scored easily at the far post after Spanish midfielder David Lopez set him up superbly by rolling the ball behind the defenders.
Recalled midfielder Rohan Ince headed a Craig Conway cross over shortly after as Brighton looked to build on their fine start.
Brighton's former England defender Matthew Upson got a crucial block to deny Jamie Vardy before Brezovan gathered a shot by Lloyd Dyer.
The Seagulls suffered a blow when skipper Gordon Greer was forced off injured in the 17th minute and he was replaced by Adam El-Abd in the centre of defence.
Leicester enjoyed a spell of possession but went further behind on 28 minutes when winger Conway, on loan from Cardiff, hit his first goal for Brighton. Lopez again set it up by crossing expertly and Conway chested the ball down before beating keeper Kasper Schmeichel with a well-placed shot.
It was Conway's first goal since the strike which clinched the Championship title for Cardiff at Burnley in April.
Brighton,with only one win from their previous five home games, ended the half on top and Upson had a header cleared from a Lopez free-kick before Lopez's shot from the edge of the area was held by Schmeichel.
Schmeichel challenged Barnes robustly to deny the Brighton striker shortly after the break and the Seagulls maintained the pressure with Liam Bridcutt firing an angled shot just wide after storming through.
Wales international midfielder Andrew Crofts tried his luck from 25 yards for the Seagulls and his testing low shot was turned round the post by Schmeichel.
Leicester got themselves back in the game on 64 minutes when Andy King rose unchallenged to head in a free-kick from Anthony Knockaert at the far post.
Brezovan then did well to tip over an effort from substitute Gary Taylor-Fletcher before saving a goal-bound shot from King.
However, Barnes restored Brighton's two-goal advantage 13 minutes from time from the penalty spot after skipper Wes Morgan gave away the spot-kick by nudging the striker in the back.