The Welshmen were finally presented with the League One trophy after substitute Febian Brandy secured their 14th away win of the campaign.
They were prevented from receiving the silverware at home last week because the outcome of Leeds' appeal against their 15-point deduction was unknown at that stage.
The West Yorkshire club's failure to overturn their punishment ensured that Swansea got their hands on the trophy at the Withdean Stadium.
Brandy, on loan from Manchester United, struck the decisive blow 12 minutes from time after an inspired double substitution by manager Roberto Martinez.
He introduced Brandy and Shaun MacDonald and the pair combined five minutes later to finally find a way past a below-strength Brighton side.
MacDonald eased away from his marker Matt Richards and pulled the ball back for the pint-sized Brandy to convert from close-range.
It was no more than Swansea deserved in a free-flowing contest overflowing with chances for both teams.
Jason Scotland could have added to his 29-goal tally early on, but the Trinidad & Tobago marksman dragged his shot wide after partner Guillem Bauza headed him clear.
Wingers Paul Anderson, on loan from Liverpool, and Thomas Butler, deputising for the rested Andy Robinson, kept the Brighton defence stretched.
Butler caused countless problems when he cut inside onto his right-foot, while it took a smart double save from Brighton keeper Michels Kuipers to foil Anderson.
The home side had opportunities of their own in the opening 45 minutes.
Top-scorer Nicky Forster looped a header just wide and nodded another good chance wide of the target.
Swansea pressed on the accelerator after the break with Kuipers coming to Brighton's rescue again by denying first Anderson and then Scotland's downward header.
But just when it seemed as if Brighton might hold out, Martinez made the changes which proved decisive.