The visitors could have clinched a shock victory in the final minute when a Bas Savage shot struck the crossbar.
There were three changes in the home line-up, with Warren Feeney, Darren Pratley and Andrea Orlandi all starting.
It was Orlandi's first start since signing from Spanish club Alaves.
Brighton's first attack in the tenth minute should have brought the game's opening goal.
Swans keeper Dorus de Vries pushed out a header from Dean Hammond straight to Nicky Forster, but his point-blank shot struck the veteran on the leg and looped over the bar.
Despite Swansea's superiority in the opening stages, the Seagulls looked dangerous when they attacked through the middle and de Vries was forced to acrobatically tip over a neat lob from George O'Callaghan on the half hour.
Another chance went begging for the visitors when Hammond out-jumped Tom Butler only to send his header high and wide.
The Swans applied early pressure in the second half but once again it was Brighton who went closest when Alex Revell struck the crossbar with de Vries beaten.
Swansea almost had the breakthrough they so badly needed when a loose ball out of defence by Savage went straight to Ferrie Bodde.
His first-time shot from 20 yards left Brighton keeper Michels Kuipers standing but struck the foot of the post and rebounded to safety.
Paul Anderson came on in the 63rd minute to play up front and ten minutes later had Kuipers scrambling across goal to scoop the ball away from danger.
Brighton almost snatched the win when Savage's shot struck the crossbar and the Swans will be hoping for a quick return from injury for Andy Robinson and Leon Britton.