A late wonder save from goalkeeper Michel Vorm earned Swansea a memorable point as Liverpool failed to win at Anfield for the third succesive game.
The Dutchman tipped over Glen Johnson's 20-yard shot in a thrilling goalless draw but Andy Carroll should have given Liverpool an early lead at Anfield.
Carroll hit the Swansea bar but the visitors may have won it when Mark Gower squandered a great late chance.
And both teams had penalty appeals turned down in a frantic second half.
Swansea's Leon Britton was fouled by defender Daniel Agger on the line of the Liverpool penalty area after breaking from midfield.
But referee Phil Dowd insisted the offence was committed outside the box.
Gower wasted the subsequent free-kick before Liverpool's dangerman Luis Suarez, who had tested Vorm on numerous occasions, claimed he was brought down in the area.
Swans right-back Angel Rangel was the covering defender in the final minute of added time but experienced official Dowd judged that Suarez was fairly challenged.
The Swans, who have never won at Anfield, impressed with their passing and possession game and deserved the draw that gives them only their second away point of the season.
England striker Carroll, however, would have been disappointed not to convert a seemingly simple chance in the opening seven minutes.
A sublime move between Charlie Adam and Stewart Downing sliced open the Swansea defence but, from just six yards out, unmarked Carroll could not apply a fitting finish from Downing's cross as his strike crashed against the crossbar.
Suarez then fired just wide but the visitors gave a signal of intent as Liverpool keeper Jose Reina's point-blank reactions were tested following a good move down the Swansea left.
Wayne Routledge beat two defenders before firing an inswinging cross into the danger zone.
And, if Danny Graham had got any kind of touch to Routledge's superb ball, then the Swans striker would have almost certainly celebrated his fifth goal in as many games.
Reina's Swansea counterpart Vorm needed his reactions to be spot on when he tipped a 25-yarder from Suarez wide before Joe Allen curled a shot wide for Swansea.
Carroll tested Vorm again with a towering header from Adam's corner as the keeper nudged the effort wide.
Suarez continued to threaten for Liverpool, who are unbeaten at home, and the Swans stopper needed to be alert to save the Uruguay striker's flicked header from Adam's inswinging free-kick.
Liverpool hearts fluttered when Reina spilled Nathan Dyer's 20-yard shot into the path of Graham but the captain made amends to block the follow-up.
Liverpool are unbeaten in six matches, their longest run since manager Kenny Dalglish returned. Liverpool have won just three of their last 11 matches against newly promoted sides
This was the first time in 16 visits that Swansea have kept a clean sheet at Anfield
And after Britton's Swansea penalty shout, the visitors, who suffered a record 8-0 defeat on their last Anfield visit in a 1990 FA Cup tie, could have snatched victory in the final minutes.
But an unmarked Gower blazed over from 12 yards after Graham's perfect knock-down from Nathan Dyer's deep right-wing cross.
Liverpool substitute striker Dirk Kuyt did put the ball in the Swans net but it was ruled out for offside by assistant referee Sian Massey.
The Vorm show concluded an entertaining game as, just moments after the Swansea keeper saved a long-range strike from Suarez, he kept out Johnson.