Chico Flores opened the scoring after 34 minutes of the fourth-round tie when he powered home via his head from a corner.
Joe Cole spurned a great chance to net an instant equaliser when he directed a weak header at goal when unmarked, while substitute Steven Gerrard rattled the post midway through the second period.
However, Swansea secured its passage into the quarterfinals when Nathan Dyer capped a counter-attack by tapping home Pablo Henandez‘s low cross at the Kop end.
Luis Suarez reduced the arrears in the 77th minute by heading in a Gerrard free-kick, but Jonathan De Guzman wrapped up a Swansea success with an injury-time strike.
The prematch team news confirmed a starting berth for 18-year-old striker Samed Yesil, while Jonjo Shelvey lined up to make his 50th Liverpool appearance.
The likes of Joe Cole, Oussama Assaidi, Joe Allen, Jack Robinson and Jordan Henderson completed the starting XI, while Brendan Rodgers named a strong bench that included Suarez and Gerrard, Raheem Sterling and Martin Skrtel.
The bitterly cold evening presented Rodgers with a first chance to pit his wits against former club Swansea since he departed the Liberty Stadium for Anfield in June.
However, the boss stressed in the build up that there would be no room for sentiment come kick off, as the Reds looked to take another step towards a successful defence of the trophy they’d held aloft at Wembley in February.
The first opening arrived in the ninth minute when the persistence of Yesil almost provided him with a route to goal, but Ashley Williams on the slide managed to thwart his advances.
Williams was soon involved at the other end, his raking ball over the top almost setting Dyer through on goal, but the winger’s touch thankfully evaded him at the crucial moment and Brad Jones was able to gather.
Ki-Sung Yeung then had the Australian goalkeeper scrambling across his goal line with a 20-yard punt, as the visitors enjoyed much of the early possession at Anfield.
Then, with 25 minutes on the clock, only the sort of last-ditch block tackle that Jamie Carragher has made his trademark over the years prevented Hernandez from a clean shot at goal after a crisp one-two between the Swansea winger and Michu had dissected the Reds’ defence.
Back came the hosts, and Stewart Downing‘s daisy-cutter from distance required turning around the base of the post by Gerhard Tremmel, but De Guzman spurned a glorious chance to open the scoring for the Swans when his attempted lob over the onrushing Jones only succeeded in finding the roof of the net at the end of a lightening counter.
However, the breakthrough did arrive in the 34th minute. After Jones had pushed Yeung’s effort out for a corner, Chico rose highest to power a header into the corner of the net and give Michael Laudrup‘s men the lead.
Liverpool could have restored instant parity had Cole been able to get any purchase on a header from Assaidi’s center when unmarked, but his attempt lacked power and bounced into the grateful gloves of Tremmel.
Yesil then saw a shot blocked and Downing fired into the hoardings, as Swansea kept a grip on its advantage heading into the break.
Just as he did in Sunday’s Merseyside derby, Rodgers made a double change during the break — this time Suarez and Gerrard came from the bench to replace Cole and Yesil.
And as Liverpool looked to take the game to its guests in the early stages of the second period, Shelvey danced his way beyond the challenge of two Swansea defenders before striking over.
The England man then teed up Suarez with a sumptuous outside-of-the-boot cross that the Uruguayan nodded off target five minutes after the restart.
Liverpool was to go closer still in the 64th minute, Gerrard’s thump from range crashing against the base of the post. It appeared the ball would bounce kindly for Downing, but the winger could not get set to covert and nudged well wide. Sterling entered the fray for Assaidi in the aftermath.
But the Reds were perhaps fortunate to survive an incredible passage of play that followed next as a goalmouth scramble saw Swansea pepper the Kop end goal repeatedly. Only the reflexes of Jones and the bravery of Carragher denied the Swans a second of the night.
Jones was then required to tip a stinging strike from Michu over the bar, and Williams powered a header inches wide from the resulting corner.
It was then Liverpool’s turn to frantically try and turn the ball home in a crowded box as Shelvey, Coates, Carragher and Suarez all tried to net.
It was unable to, however, and within seconds Swansea doubled its advantage as it broke forward, resulting in Dyer tapping in Hernandez’s cross.
Liverpool’s retort was an instant one, as Suarez strode into space to head in Gerrard’s free-kick with 13 minutes remaining.
But despite heavy late pressure, the Reds were unable to conjure up a dramatic equaliser as the Swans clinched victory with De Guzman’s last-gasp tap in.
Liverpoolfc.com journalists’ man of the match: Brad Jones