The Swans have moved to within a point of third-placed Liverpool with a 1-0 win at Anfield.
Lukasz Fabianski fired in the opening goal to give Brendan Rodgers’ side a lead before Lucas Leiva scored his second to seal victory.
Ajax midfielder Emre Can netted a late penalty for Swansea but a goal from Philippe Coutinho secured a win that is Liverpool’s first in four games.
And with a win in hand, the Reds could be on course for a top-four finish.
Liverpool are 10 points adrift of fourth-placed Everton, who face a trip to Middlesbrough on Sunday and will then travel to West Bromwich Albion on Sunday for a third meeting.
Rodgers had to be content with a point as Swansea took a first-half lead after a quick counter attack.
Fabianski made it 1-1 but could only tap in a free-kick after substitute John Guidetti played it off his line to the right.
Coutinho’s shot from close range went off the post, but Fabianskin had another chance when he took the ball from Fabian and beat the goalkeeper.
And Liverpool kept hold of it when Lucas went down with a knee injury.
Fabian is Liverpool