Stephen Dobbie's brace and a first-half strike from Garry Monk handed new Swans manager Paulo Sousa his first competitive win in charge at the Liberty Stadium.
Skipper Monk opened the scoring in the 16th minute after the defender reacted quickest to head home after Alan Tate flicked Andrea Orlandi's free-kick onto the post.
Swans spurned several chances to increase their lead through Nathan Dyer and Mark Gower before Scottish striker Dobbie opened his account with a double after the break.
Dobbie, who made the summer switch to south Wales from Queen of the South on a free, fired home following Orlandi's left wing cross on the hour mark before sealing a convincing win in injury-time.
Both sides began their league campaigns with defeat, Swansea going down 2-1 at Leicester City while Brighton suffered a 1-0 home loss to Walsall .
In response, Sousa made five changes after leaving the Walkers Stadium empty-handed with Dobbie, Jordi Lopez and Andrea Orlandi stepping up from the bench while Federico Bessone and Matty Collins occupied the full-back berths.
Joe Allen was ruled out for three weeks with a hamstring problem to join injured midfield duo Ferrie Bodde and Darren Pratley on the sidelines.
Swansea took a deserved lead on 16 minutes when Tate glanced Orlandi's free-kick past Brighton goalkeeper Michel Kuipers before Monk produced the finishing touch.
Monk's opposite number Adam Virgo had the chance to level the scores a minute later but the former Celtic centre-back saw his header drift wide.
Brighton manager Russell Slade made a double substitution at the break, introducing Adam El-Abd and Mark Wright.
But despite the changes, the visitors failed to inject any life into a disappointing display as Swansea increased their lead.
Dobbie's initial effort ricocheted off a Brighton defender but Swansea 's newest hitman was sharp enough to poke home the rebound.
Then Dobbie made it three when he latched onto Guillem Bauza's cross to coolly flick the ball over Kuipers in injury-time to seal a fine personal evening's work.