Jordan Henderson scores the winner in the middle of the second half to close the gap on 4th placed Manchester United to 2 points, ahead of next week's Anfield clash.
Liverpool welcomed back Mamadou Sakho into the starting line up and Steven Gerrard returned to the bench. Mario Balotelli missed out of a squad place due to illness.
The reds were poor for the vast majority of the first half, and a string of saves from Mignolet coupled with last ditch tackles by Skrtel and Allen and clearances by Sakho meant the reds were very lucky to go to the break at 0-0.
The reds were better second half as they altered their tactics to deal with Swansea's midfield diamond.
Sterling and Lallana saw far more of the ball and the reds passing improved hugely. Shortly after the hour the reds brought on Gerrard allowing Henderson more freedom to go forward.
And within moments of the change Henderson powered forward - the goal firing in off his shin as Jordi Amat attempted to challenge him.
Since the reds last league meeting with Manchester United the reds form has improved hugely. Liverpool have collected 33 points from the last 13 games (10 wins and 3 draws).
Next weekend Liverpool host United at Anfield with the opportunity that victory would move the reds into the top four.