The Reds had won their last five successive games and had not lost since October 22 but served up a lacklustre display in South Wales and could not respond to defender Alfie Mawson's supreme finish from a first-half corner following an unfortunate defensive mix-up.
Liverpool dominated possession throughout but could not pry the hosts open, lacking their usual fluid combinations and class in front of goal with Mohamed Salah and Sadio Mané wasting two of their clearest chances.
Roberto Firmino also crashed a late header against the post before substitute Adam Lallana could not convert the follow-up due to Mawson's excellent block, with Liverpool failing to score despite 21 attempts and 72 per-cent possession.
The Swans produced a superb defensive display and have now lost only one of six games in all competitions since Carlos Carvalhal's appointment just days after their 5-0 Boxing Day reverse to Liverpool.
Swansea remain bottom of the top-flight table due to their goal difference but are just three points from safety while Liverpool stay in fourth but missed a chance to move level on points with Chelsea in third and to further the gap between themselves and top-four rivals Tottenham Hotspur and Arsenal.
Reds dominate but struggle for openings
Liverpool took time to find their rhythm early on but demonstrated their threat when Emre Can picked out Mané inside the box with a lofted pass. The winger's heavy touch however allowed Łukasz Fabiański to gather.
The Swans showed a surprising early intent to attack but when Liverpool were in possession congested their own third thanks to their five-man defence and sturdy organisation.
In spite of the Reds' forward firepower it was Virgil van Dijk - making his first Premier League appearance for the club - who spearheaded Liverpool's best spell, heading wide after rising highest to Alex Oxlade-Chamberlain's corner.
The Dutch centre-back, 40 yards from goal, then lifted a pinpoint pass over the top into Salah but the Egyptian could only volley a first-time effort over the crossbar as he spun towards goal.
Van Dijk's defensive partner Joël Matip also strode forward as Liverpool looked to counter-act Swansea's sheer numbers at the back, with his run culminating in the game's first shot on target from Oxlade-Chamberlain - though Fabiański held his drive easily.
Mawson capitalises on miscommunication
Swansea struggled from open play with Kyle Naughton volleying well over but netted the opening goal from a corner on 41 minutes with Liverpool's set-piece defending again coming under scrutiny.
Jürgen Klopp's men failed to deal with the second ball after four defenders simultaneously attempted to head clear, with Van Dijk only able to head the ball down to Federico Fernández. It flicked up off the defender and fell to Mawson to rifle a low effort into the bottom corner with the poise and precision of a top-tier striker.
Liverpool should have responded in first-half injury time when Salah raced forward on the counter and chipped centrally to Mané, who could not keep his volley on target as he stretched to shoot.
The Merseyside club responded well after the interval though Joe Gomez's intervention was required to prevent Jordan Ayew from breaking into the box after a promising Swansea counter.
Liverpool increased their pressure and Naughton's last-gasp stretch denied Andrew Robertson a clear attempt inside the area, poking the ball just out of the Scot's reach with excellent timing.
Reds press to draw level but fall short
Salah almost slipped through Firmino soon after only for Fabiański to sprint off his line and beat the forward to his through ball before testing the Polish 'keeper with a free-kick he had to tip over the bar.
Yet despite netting 85 goals across all competitions this season - including an unparalleled 29 in 11 Premier League away games - they struggled for composure in front of goal as the game wore on.
Danny Ings was handed just his third appearance of the season off the bench and forced a low save from Fabiański on 77 minutes, but despite battling until the final whistle, Liverpool could not rally for an equaliser and drew a rare blank.
Even the excellent Salah wasted a great chance late on at the near post, blazing wide with team-mates in the box with Liverpool missing their usual quality going forward and being made to pay the price.
Firmino headed against the woodwork deep into stoppage time from a Van Dijk cross with Lallana then denied by Mawson on the goal-line.
Liverpool's frustrations spilled over after the full-time whistle but they could only be angry at themselves for such an underwhelming performance riddled with poor decision-making and substandard execution.
Swansea will hope this win can act as the catalyst for an improved run of form as they look to once again avoid the drop down to the Championship, and the early signs under Carvalhal suggest that they are well capable of doing so.