The Swans were made to rue missed chances as a fortuitous Jordan Henderson goal earned Liverpool a 1-0 victory at the Liberty Stadium.
Garry Monk's side enjoyed the better of the chances during a frenetic first period as Gylfi Sigurdsson and Bafe Gomis were both denied by Liverpool goalkeeper Simon Mignolet.
But the visitors were much improved after the restart and took the lead on 68 minutes when Jordi Amat's attempted clearance was deflected into the net by Henderson.
Daniel Sturridge had a chance to double Liverpool's lead late on, as the visitors caught the Swans on the counter, but his side-footed effort hit the post.
The narrow defeat means Garry Monk's side remain ninth in the table on 40 points.
The Swans made one change to the side that suffered a narrow 3-2 defeat at Tottenham Hotspur last time out as Jordi Amat comes in for Federico Fernandez, who is absent tonight due to family reasons.
SWANS: Lukasz Fabianski, Kyle Naughton, Jordi Amat, Ashley Williams (capt), Neil Taylor, Jack Cork, Ki Sung-Yueng (Nathan Dyer, 80), Jonjo Shelvey, Gylfi Sigurdsson, Wayne Routledge (Jefferson Montero, 73), Bafetimbi Gomis. (Marvin Emnes, 89)
SUBS: Gerhard Tremmel, Angel Rangel, Leon Britton, Nelson Oliveira.
LIVERPOOL: Simon Mignolet, Emre Can, Martin Skrtel, Mamadou Sakho, Raheem Sterling, Jordan Henderson (capt), Joe Allen, Alberto Moreno (Steven Gerrard, 64), Adam Lallana (Glen Johnson, 87), Philippe Coutinho, Daniel Sturridge.
SUBS: Brad Jones, Kolo Toure, Dejan Lovren, Lazar Markovic, Rickie Lambert.
After a cagey opening to proceedings, the first chance of the game fell the visitors' way as Daniel Sturridge dragged an effort wide of goal after finding space on the edge of Swansea's 18-yard box.
But Swansea's high-pressing game seemed to cause the Liverpool defence some problems as Ki Sung-Yueng and Bafe Gomis both had headed efforts cleared by Martin Skrtel after Garry Monk's side were able to dispossess the Reds.
It wasn't until the half-hour mark that either goalkeeper was tested, though, as Simon Mignolet was first called into action to push away Bafe Gomis' driven effort, before Gylfi Sigurdsson saw an effort curl just over following a clever turn inside the box.
The Icelandic midfielder then went even closer as his fizzed effort looked to have found the top corner, only for Mignolet to tip his effort wide.
And the chances were coming thick and fast for the hosts as Jonjo Shelvey then saw a first-time effort diverted just wide via the head of Adam Lallana.
HALF-TIME: Swans 0 Liverpool 0
Just over ten minutes into the restart, Lukasz Fabianski was forced into his first save of the night as the Polish shot stopper turned Philippe Coutinho's first-time effort around the post.
After Sigurdsson saw a free-kick comfortably saved by Mignolet, Fabianski was then called into action once again to keep out Joe Allen's effort from close range.
Despite the home side boasting the majority of the chances, it was the visitors who took the lead in SA1 as, rather fortuitously, Jordi Amat's attempted clearance was deflected into the net off Jordan Henderson on 68 minutes.
With 15 minutes left of play, Raheem Sterling squandered a chance to double Brendan Rodgers' side's lead, hitting over the bar from Sturridge's neat ball over the top.
In an attempt to find a way back into the game, substitutes Jefferson Montero and Marvin Emnes were introduced, but the Swans were nearly caught on the counter, only for Sturridge's low effort to hit the post.