Swansea produced a fine away performance to earn a famous point at Anfield as Liverpool went three games without a win at home.
Andy Carroll hit the crossbar and Luis Suarez was denied by Michel Vorm as the home side shaded an even first half, despite Joe Allen coming a whisker away from giving the Swans the lead with a curling shot.
But the visitors pressed hard in the second period as Danny Graham was denied by Pepe Reina, before Mark Gower should have won the game for Swansea after firing over from Graham's knock down.
However, Liverpool pushed for a winner with sub Dirk Kuyt seeing his late effort ruled out for offside. The hosts continued their search for the winner in stoppage time but were denied by the heroics of Vorm and some valiant defending as the Swans cemented their place in the top half of the Premier League.
Brendan Rodgers made one change to the side that beat Bolton the previous weekend as Wayne Routledge came in to replace Scott Sinclair, who had a slight hamstring problem.
The winger dropped to the bench where he was joined by the returning Kemy Agustien, who had been out since injuring his hamstring in the defeat at Arsenal in September.
Meanwhile, Liverpool boss Kenny Dalglish named the same starting line-up that won comfortably at West Bromwich Albion, with record signing Andy Carroll partnering Luis Suarez in attack.
Liverpool: Jose Reina, Glen Johnson, Martin Skrtel, Daniel Agger, Jose Enrique, Jordan Henderson (Dirk Kuyt, h/t), Charlie Adam, Lucas, Stewart Downing, Luis Suarez, Andy Carroll (Craig Bellamy, 75)
Subs not used: Doni, Maxi Rodriguez, Sebastian Coates, Jay Spearing, Martin Kelly
Swans: Michel Vorm, Angel Rangel, Ashley Williams, Garry Monk, Neil Taylor, Leon Britton, Mark Gower (Kemy Agustien, 90), Joe Allen, Wayne Routledge (Scott Sinclair, 74), Nathan Dyer, Danny Graham
Subs not used: Gerhard Tremmel, Vangelis Moras, Jazz Richards, Leroy Lita, Luke Moore
Referee: Phil Dowd
There was a terrific atmosphere inside Anfield as the home side got the game underway.
After the Swans had made a confident start in front of the Kop, it was the home side who should have taken the lead on 7 minutes when Stewart Downing latched onto a ball down the left flank and his low cross was met by Andy Carroll whose left foot shot cannoned back of the crossbar.
But the visitors responded well and after 16 minutes had a spell of possession in and around the Liverpool box which ended with Angel Rangel firing high and wide from 20 yards.
Liverpool came back strongly five minutes later when first Suarez fired just wide from 25 yards and then Downing saw his strike deflected over by Rangel.
The hosts were now starting to grow into the game and they had another chance on 24 minutes when Jose Enrique's cross was met by the diving Lucas, but the Brazilian could only divert his header wide of Michel Vorm's goal.
But on 28 minutes the Swans had a great chance to open the scoring when Routledge tricked his way past two defenders down the left and his cross was flicked goalwards by Danny Graham and Jose Reina did superbly to tip the ball away.
Just a minute later and the home side created their best chance of the game so far when Suarez jinked his way past Garry Monk inside the box and his curling effort looked destined for the bottom corner until Vorm flung out a hand to parry the ball behind.
But the Swans responded once more on 38 minutes and after a wonderful passing move that started in their own half, Joe Allen turned his man on the edge of the box and his curling effort flew just wide of Reina's left hand post.
And in first half stoppage time Liverpool could have taken the lead when Carroll met Adam's deep corner, but the England international saw his effort parried away by Vorm.
Half-time: Liverpool 0 Swans 0
The home side made their first change during the half time interval as Dirk Kuyt came on for Jordan Henderson.
Liverpool came out much brighter in the second period than they did in the first as they looked to get the all important opening goal.
And the first chance of the half fell to the home side as Carroll met Adam's inswinging free kick, but his header was well saved by Vorm.
But the Swans held firm and came close to opening the scoring themselves when Enrique's backpass put Reina in trouble but the Spaniard managed to scramble the ball away to safety.
The visitors then created a good opening when Routledge slipped in Dyer but the winger's effort was foiled by a good block from Reina.
Swansea then created their best chance of the game so far on 66 minutes when Dyer again cut in from the right and as his effort was parried by Reina, Graham closed in to follow up the rebound but his shot was superbly blocked by the 'keeper once more.
The visitors then made their first change of the afternoon as Scott Sinclair came off the bench to replace the tireless Routledge.
Liverpool then nearly took the lead against the run of play when Kuyt played a one-two with Suarez, but his run was halted with a last ditch challenge from Ashley Williams.
And from the corner that followed, Vorm could only punch the ball away and Martin Skrtel headed towards goal but his effort ended up on the roof of the net.
Liverpool then came a whisker away from taking the lead after 82 minutes, when Charlie Adam's fre kick from the edge of the box was deflected a fraction wide of Vorm's right hand post.
But then the Swans had a golden chance to take the lead as Dyer's far post cross was headed back across goal by Graham for the onrushing Gower and he lashed his volley over from eight yards with the Liverpool defence nowhere to be seen.
Then Swans hearts were so nearly broken two minutes from time as the home fans thought their side had taken the lead.
Charlie Adam's corner was cleared away and as Glen Johnson lifted the ball back in the ball looped up and Kuyt stooped low to head the ball past Vorm, only for assistant referee Sian Massey to flag for offside.
That started a period of sustained pressure from the home side, as Suarez fired a shot at goal from 20 yards that Vorm had to deal with at full stretch, before Johnson then struck a powerful volley from just inside the box that the Dutch keeper did superbly well to tip over the ball.
But as the fourth official indicated four minutes of time added on, the Swans defence held firm to hold out for a thoroughly deserved point and left the field to a chorus of applause from the home crowd.