The Reds brought on the big guns after falling behind to Chico Flores but Nathan Dyer and Jonathan De Guzman put the tie out of their reach to spoil ex-boss Brendan Rodgers' night
Chico Flores' goal from a corner was just reward for a first-half points victory on the visitors' part, while Luis Suarez's swift reply to Nathan Dyer's second-period tap-in was not enough for the Reds as Jonathan De Guzman confirmed the upset in injury time on a similar break.
Joe Allen lined up against his former side and Samed Yesil made his second starting appearance for Liverpool while Stewart Downing and Joe Cole were amongst nine changes. Michael Laudrup, meanwhile, named a close-to-full-strength team.
A low-key start saw both sides surrendering possession easily but the Swans upped their game after the quarter-hour. The energetic Pablo Hernandez came close to an opener as he combined with Michu but Jamie Carragher got in to make an important block.
De Guzman might have scored as well, chipping over when simple would have been better after great work on the wing from Dyer.
Though Downing probed, the Swans' dominance turned into a lead. De Guzman's corner was weighted perfectly for Chico and the Spaniard nodded home with little fuss. At the other end, Cole missed a chance to reply with a weak header.
Liverpool needed a big improvement at the break and Rodgers duly summoned Steven Gerrard and Luis Suarez. The change immediately livened the hosts up but the Uruguayan took just two minutes to miss his first chance, heading over from Jonjo Shelvey’s cross.
There was a blow for Swansea as goalscorer Chico succumbed to an injury, Garry Monk replacing him in central defence, and the Reds smelled blood.
Gerrard surged forward just past the hour and his low, powerful effort rebounded off the post. With Tremmel in no-man's-land, Downing should have put it away but awkwardly pulled it wide instead.
After a series of Swansea shots were blocked and Ashley Williams headed over, Liverpool looked like punishing their profligacy with a dangerous free kick bounced dangerously but failed to convert and paid the price.
A sensational break provided the visitors' second, Michu supplying Hernandez, who raced ahead before putting it on a plate for Dyer. The two-goal cushion did not last long, though.
The substitutes combined to give the hosts hope, Gerrard swinging in the free kick and Suarez getting his header right this time to flick home.
Liverpool were increasingly desperate and, after Michu twice nearly broke free for a third, Suarez nearly wriggled his way into emulating his opener from the Everton match but was blocked this time around.
A generous five minutes of added time were provided but the Reds only used it to let Swansea free on the counter, Michu wrapping up a fine game by setting up De Guzman to confirm that it will be a different name on the trophy this season.