Burnley deservedly went ahead in the 21st minute as Netherlands striker Wout Weghorst claimed his first goal for the club.
Aaron Lennon released Connor Roberts down the right and his cut back was clinically swept home by January signing Weghorst.
The Clarets had earlier struck the crossbar through Roberts.
The Clarets doubled their advantage five minutes before half-time.
Brighton failed to deal with a long ball forward, leading to Josh Brownhill sending a low, deflected effort beyond goalkeeper Robert Sanchez.
Burnley looked to have put the result beyond doubt with just over 20 minutes remaining when Aaron Lennon burst into the box to lash home.
Scroll down and click through to see Sonny Turner's player ratings from the Amex Stadium.
1. Rob Sanchez 4
Unlucky with the goals conceded. A drilled effort from Weghorst, a Brownhill deflected shot, and a fantastic top corner finish by Lennon, all of which he had little chance to keep out, in what was an unenjoyable afternoon for the Brighton ‘keeper.
2. Tariq Lamptey 4
Was caused trouble by Dwight McNeil early in the game, and didn’t get across to Weghorst in time for the Burnley opener, when he ought to have read the danger. Did provide some attacking threat down the right hand-side.
3. Shane Duffy 3
Was bullied by Weghorst throughout the game, and lacked mobility against Rodriguez. Failed to get anywhere near Lennon to block the shot for the third goal. A poor display.
4. Joel Veltman 4
Gave cheap fouls away throughout the game, from which Burnley posed a threat. Failed to contain Weghorst, and did little to stop Burnley from cracking in three goals.