Ivan Juric has won his first game as Southampton manager against Russell Martin's old club, helping the Saints to a fourth round draw at home to Burnley.
Just 12,000 people were at St Mary's to see the Premier League's bottom club beat Luke Williams' side thanks to a brilliant performance from Kamaldeen Sulemana.
The Ghanaian scored the opening goal, his first since May 2023, and set up the second goal for Tyler Dibling, who scored again in the second half.
Saints had made just two changes, Swansea four and it was the Premier League strugglers who dominated from start to finish.
Kyle Walker-Peters came close early with a left-foot shot in the tenth minute, while Sulemana shot just wide a minute later.
Walker-Peters found enough space on the right and went close again after being released following a driving run from Matheus Fernandes.
A Saints goal seemed inevitable and came via the most direct route. A long kick-up from Aaron Ramsdale was started by Lesley Ugochukwu and Sulemana cleverly lobbed it to the stranded Jon McLaughlin.
Swansea struggled to pose any threat to Ivan Juric's side and the Saints were two up ten minutes before half-time when the lively Sulemana raced to the byline and pulled the ball across for Dibling to tap home .
Shortly after the break, more opportunities followed for Saints. Only a straight save from McLaughlin could prevent Jan Bednarek from heading into Ryan Manning's corner.
It was 18-year-old Dibling who scored the third, scoring from Manning's low cross at the second attempt after Kyle Naughton had failed to clear the ball.
Cameron Archer should have made it four after being taken out by Fernandes but McLaughlin stood his ground and denied him.
The small group of supporters who had come from South Wales almost had something to cheer about when Joe Allen hit the post after a Will Smallbone error, but Southampton kept a rare clean sheet.
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