Another Darryl Duffy double fired the Swans to a hard-earned victory at the Liberty Stadium that moved them a step closer to the League One play-offs.
Duffy, who also scored twice against Port Vale at the Liberty a fortnight ago, struck the crucial blows before the break as the Swans had to come from behind against a spirited Brighton team.
It proved a good day for Roberto Martinez's men as they moved level on points with sixth-placed Oldham who lost 2-1 at Crewe.
Eighth-placed Carlisle also slipped up as they went down 3-1 at home to Bristol City.
Swansea City: Gueret, Tate (c), Painter, Lawrence, Iriekpen, Britton, Craney, O'Leary, Robinson, Trundle, D Duffy. Subs: Oakes, Williams, Amankwaah, Austin, Abbott.
Brighton: Flinders; Mayo, El-Abd, Hart, Rehman, Butters (c), Rents; Bertin, Cox, Savage, Revell. Subs: Kuipers (GK), Elder, Elphick, Ward, Robinson.
Ref: Ray Olivier
Asst-refs: A M Turner, A S Watts, A Williams
4th official: A Williams
Att: 11,972
The Swans, three points off sixth-placed Oldham, were looking for a maximum haul to take into their final two games against Carlisle (a) and Blackpool (h) in a bid to snatch a play-off place.
Manager Roberto Martinez welcomed back Andy Robinson from a hamstring injury. He came straight into midfield in place of the injured Tom Butler.
Alan Tate also returned to the side at right back instead of Richard Duffy. Tate was also given the captain's armband in place of Lee Trundle who started up front alongside Darryl Duffy.
They were the only changes to the side that drew 2-2 at Bournemouth last Saturday.
Brighton, sitting in 16th place bust still not mathematically safe from relegation, were again without defender Joel Lynch who missed last week's defeat by Bradford with glandular fever.
On-loan QPR utility player Zesh Rehman continues alongside Guy Butters in the heart of the defence.
Striker Alex Revell continued up front despite suffering with a hernia problem.
Swansea made a bright opening as Kristian O'Leary flashed a low drive from the edge of the area just wide of the far post.
But the home side then went on to give a lot of possession away in the opening 10 minutes and were punished in the 14th minute when Brighton took a shock lead.
Andy Robinson gave away a clumsy free-kick near the corner flag and when Sam Rents delivered it, Alex Revell found himself free inside the six-yard area to head beyond Willy Gueret.
Swansea nearly equalized straight from the kick off. Referee Ray Olivier allowed Swansea to kick-off while Brighton were still celebrating and Trundle broke through only to see his shot headed off the line for what would have been a controversial equalizer.
Swansea were level in the 21st minute, however, when Tate's header back in eluded the Brighton defence and Darryl Duffy pounced to send a looping header over Scott Flinders for his third goal in as many games.
Izzy Iriekpen had to be alert to head a goal-bound effort away after substitute Jake Robinson, on for the injured Bas Savage, looped a cross over Gueret.
Swansea hit straight back when a tremendous run from Trundle took him to the by-line before delivering a deep cross which Leon Britton did well to head back. Robinson met it, but his shot was blocked for a corner.
Robinson delivered it only for Iriekpen's thumping header to fly just wide.
Swansea were starting to enjoy themselves now as Trundle tormented Alexis Bertin before Dennis Lawrence, Britton and Tate tried their luck as Brighton failed to clear their lines.
And with Roberto's men improving all the time, they took a 2-1 lead with 42 minutes gone.
A long ball from Robinson picked out Duffy on the edge of the area and the loan-signing from Hull produced a tremendous turn and shot which flew into the bottom corner for his second of the afternoon.
Half-time: Swans 2 Brighton 1
Tom Williams replaced the injured Marcos Painter at left-back for the start of the second-half.
Ian Craney lobbed an early shot over Flinders' bar before Swansea were given a 5oth minute scare.
Gueret came out to the edge of his area to make a good save from Robinson, but the linesman claimed the Swansea 'keeper picked the loose ball up outside his area. Fortunately for Swansea, Tate managed to clear Brighton's well-worked free-kick.
Trundle responded with a clever chip which dropped onto the roof of the Brighton net as Swansea went in search of the third goal to kill the game off.
Brighton weren't prepared to give up without a fight, however, and enjoyed a good spell on the hour without troubling Gueret.
Roberto responded by bringing on Kevin Austin for Robinson. Austin moved into the left-back spot with Williams pushing on into midfield.
Austin was straight into the action as he cleared the danger from a Brighton free-kick with the visitors claiming a penalty for handball with 65 minutes gone.
While Swansea were still looking dangerous going forward, Brighton were proving more than a match as Dean Cox struck the post with 16 minutes remaining.
Then with just two minutes remaining, Gueret had to produced two great saves from substitutes Nathan Elder and Nick Ward to prevent Brighton snatching a late share of the spoils.
