Aaron Connolly scored both goals for the Seagulls as they continue their excellent play that has seen them win six of seven games in all competitions.
Story of the match
Swansea were first on the attack as Whittaker saw his shot blocked. A cross from Jake Bidwell skimmed was only cleared as far as Walsh and he sent a lovely first-time pass to Liam Cullen, his effort deflected out for a corner.
The resulting set-piece saw Smith find Bidwell and his teasing cross was met by the head of Williams, but he could only direct his attempt straight at Brighton keeper Jason Steele.
Bidwell then sent in another cross that found Smith, but he could only skim his header past the post and at the other end, Cooper's loose pass was pounced on by the Seagulls, Williams seeing off the danger.
The hosts were struggling to create anything in the final third, but their first shot on target gave them the lead. A perfectly weighted pass from Alexis Mac Allister released Connolly down the left and he dinked over Swans goalkeeper Steven Benda.
Five minutes later, the defender doubled Brighton's lead as the Swans lost possession in midfield. Mac Allister pounced, sent in a pass for Connolly and he turned inside of Williams, slotting past Benda and into the far corner.
Three minutes into the second half, Swansea nearly halved the deficit as Cullen got on the end of Whittaker's cross, but his side-footed shot from eight yards out hit the crossbar.
Cullen and Smith then combined to set up Whittaker, who was denied by Steele. The Seagulls goalkeeper then played a short pass that Jay Fulton slid in to send to Cullen and he touched for Smith, who found the crossbar.
Brighton could have added a third as a free-kick by Pascal Gross in stoppage time deflected off of the wall and onto the bar, that being the last action of the contest as the hosts eased into round four.
Man of the match: Aaron Connolly
In truth, Brighton didn't create very many chances, but the two that presented themselves to Connolly were taken with class and it was enough to help the Seagulls move on in the competition.