Both sides have both been in decent form over the past few weeks and it was an absorbing game from the start, with Liverpool carving out the better chances in the first half but unable to break the deadlock.
The closest they came was just after the half-hour mark, when Raheem Sterling was denied by the width of the crossbar as he thumped a ferocious volley against the woodwork.
Jose Enrique also had a goal disallowed for offside after sliding in on Luis Suarez's cross, while Glen Johnson headed over from a corner before being thwarted by a Gerhard Tremmel stop.
Swansea played their part, though, with Pepe Reina forced to produce a good save from Wayne Routledge's strike and Pablo Hernandez curling a delightful effort narrowly wide from outside the area.
Michael Laudrup brought Ki Sung-yueng on for the anonymous Itay Shechter at half-time and pushed Michu up front in an effort to alter the pattern of the game.
It worked to some extent as Michu's header was kept out by Reina and Routledge and Michu both had penalty appeals turned down, while Ashley Williams also had an effort cleared off the line during a good spell for the home side.
There was an injury scare for Reina when he rushed off his line and was clattered into by Nathan Dyer, as the match stretched from end to end with both teams hunting for a winner.
Spain winger Hernandez had a low-free-kick brilliantly tipped wide by Reina, but Liverpool looked dangerous on the counter-attack and had a chance when Suarez and Sterling broke from a Swansea corner and had only Ben Davies in front of them, but a laboured pass from the winger forced the Uruguayan wide and Tremmel held his shot.
The Reds nearly snatched a last-gasp goal when Jonjo Shelvey's drive was repelled by Tremmel, and the referee waved play on after Steven Gerrard went down under pressure from Chico.
In the end both sides had to settle for a point apiece and a result which keeps them in mid-table, with Liverpool now unbeaten in eight but still one point behind Swansea.