Liverpool moved within two points of the Champions League places and stretched their unbeaten run to 13 league games with a hard-earned win at Swansea.
Swansea dominated the first half but, thanks to Simon Mignolet's fine saves from Bafetimbi Gomis and Gylfi Sigurdsson, it was goalless at the interval.
Liverpool were vastly improved after the restart and scored a fortuitous winner when Jordi Amat's clearance deflected off Jordan Henderson and into the net.
The Reds remain fifth in the Premier League table but are just two points behind fourth-placed Manchester United, who they host on Sunday.
The mouth-watering prospect of that match at Anfield served as inspiration for Liverpool, who were aiming to seize on the indifferent recent form of their rivals for the top four.
There was also the matter of personal pride for manager Brendan Rodgers, returning to the club he managed for two years before moving to Anfield in 2012.
Rodgers' final game in charge of Swansea was a 1-0 victory against Liverpool a month before his move.
The Swans, who have not beaten Liverpool in the league since then, were aiming to become the first team to beat the Reds in the Premier League in 2015, and they made a purposeful start.
Their fluid five-man midfield controlled possession early on, while Gomis had the first genuine chance as his low shot was pushed away by Mignolet.
The Belgian goalkeeper produced an even better save five minutes later, stretching to turn a curling effort from Sigurdsson around the post.
Having been in such fluent form lately, Liverpool were restricted to a couple of hopeful long-range shots by Philippe Coutinho and Daniel Sturridge.
Their frustration was typified by yellow cards for Henderson and Raheem Sterling but, having withstood so much pressure, they might have been relieved to enter the break on level terms.
Liverpool emerged for the second half a different team, with Coutinho and Joe Allen both forcing Lukasz Fabianski into saves.
Rodgers' side increased the tempo and, moments after bringing on club captain Steven Gerrard, they took the lead in fortuitous circumstances.
Henderson bore down on goal and, although Amat got to the ball first, his sliding clearance hit the Liverpool midfielder and looped into the net.
The visitors took control from that point and, while Sturridge could only hit the post when well set in injury time, Liverpool were ultimately comfortable winners as they sealed a 10th win in 13 league games.
Simon Mignolet's first-half save from Gylfi Sigurdsson helped ensure a sixth successive away league clean sheet
Steven Gerrard returned as a second-half substitute after a month out with a hamstring injury
Daniel Sturridge - who has hit three goals since returning from injury in late January - hit the post for Liverpool
Brendan Rodgers's Liverpool side have taken 32 points from the last 36 available
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