Swansea City eased their mini-slump as Scott Sinclair and Danny Graham struck in the second half to beat Fulham.
But keeper Michel Vorm was instrumental in Swansea securing their first win in five games as he saved a Clint Dempsey penalty to seal a seventh clean sheet.
Sinclair gave Swansea the lead when his weak shot was deflected into his own net by Dempsey.
Vorm then saved the American's spot-kick before sub Danny Graham nudged in Mark Gower's injury-time corner.
The win saw the Welsh club leapfrog Fulham to move up to 11th in the Premier League table as their excellent home form this season continued with a fourth Liberty Stadium win. Only reigning champions Manchester United have won in south Wales this season.
Rodgers delighted with deserved three points
And, while Sinclair and Graham got the goals, Vorm was Swansea's hero as the Dutch keeper made a string of fine saves from Bryan Ruiz, Andy Johnson and - most dramatically - Dempsey's late penalty to ensure victory for Swansea.
Swansea had the first sight of goal in a first half of few chances but, after finding space between Brede Hangeland and Philippe Senderos, Leroy Lita headed Gower's right-wing cross wide from 10 yards.
Luke Moore went even closer a few moments later as he hit the crossbar with a 25-yard strike.
But Fulham keeper Mark Schwarzer's comfortable save from Sinclair's weak effort was the only time a goalkeeper was called into action before the break.
Swansea v Fulham fact file
Swansea kept their sixth clean sheet at home, the best tally in the Premier League
Swansea have won all of their home games when scoring first
Swansea have conceded just two goals at home this season, the lowest in the Premier League
Fulham have scored just four goals on the road this season, equal fewest in the Premier League
The second half, however, was a completely different story as Swansea broke the deadlock six minutes after the break, a huge deflection off Dempsey's leg diverting Sinclair's shot past a helpless Schwarzer.
Fulham, who were without striker Bobby Zamora, had failed to clear Gower's corner before Wayne Routledge's miscued ball fell to Sinclair and his seemingly innocuous effort was turned in by Fulham's top scorer.
Sinclair will claim his first goal from open play this season but Schwarzer seemed to have the England Under-21 winger's shot covered until Dempsey's intervention.
Dempsey almost made amends immediately as his defence-splitting pass set up Ruiz, but Vorm reacted superbly to ensure his side remained in front.
The woodwork rescued the visitors when Swans substitute Kemy Agustien hit Schwarzer's right-hand upright with a 25-yard shot just 90 seconds after coming on.
Fulham were awarded a penalty by referee Jon Moss with four minutes remaining. The London side's Swiss midfielder Kerim Frei was fouled by Swansea's left-back Ashley Richards as he burst into the area.
Jol feels Fulham deserved a point
But Vorm, proving a bargain buy following his
£1.5m summer move from FC Utrecht
, denied Dempsey with a stunning save diving to his right, his second penalty save this season.
Graham then completed the victory as the £3.5m summer signing flicked in his fifth goal in eight games at the near post from Gower's low right-wing corner.
Swansea City manager Brendan Rodgers praised Vorm's display:
"People will tell you that a good goalkeeper will get you up to 10-plus points and everyone knows we have a top keeper.
"It was a great bit of business for us, it's a steal. That penalty was a key moment, although it wasn't a penalty. If you look at the replay you can see that Jazz Richards doesn't do anything and the guy kicks his leg, goes over and the referee bought it."
Fulham manager Martin Jol:
"I think we did enough to get a point as after the own goal, we livened up and could have scored a couple of goals. But it wasn't to be.
"I don't regret not starting Bobby Zamora as we've had a lot of games where we've had clean sheets so it was about the defence not only about the strikers so I made the decision on Thursday to play Andy Johnson."
Full Time The game is over, as the referee blows his whistle.
Outswinging corner taken by Andrew Johnson from the right by-line played to the near post, clearance made by Danny Graham.
Carlos Orlando Sa takes a shot. Save by Michel Vorm.
Short corner taken by Andrew Johnson.
The assist for the goal came from Mark Gower.
90:00 +0:57 Goal scored
Goal! - Danny Graham - Swansea 2 - 0 Fulham Danny Graham finds the net with a goal from inside the penalty area low into the middle of the goal. Swansea 2-0 Fulham.
Outswinging corner taken right-footed by Mark Gower from the right by-line to the near post,
Carlos Orlando Sa gives away a free kick for an unfair challenge on Kemy Agustien. Michel Vorm restarts play with the free kick.
Substitution Wayne Routledge goes off and Nathan Dyer comes on.
Corner taken right-footed by Bryan Ruiz to the near post, Kemy Agustien makes a clearance. Bryan Ruiz takes a shot. Save made by Michel Vorm.
Penalty taken by Clint Dempsey is saved by Michel Vorm. Swansea 1-0 Fulham.
Booking Michel Vorm goes into the book for time wasting.
Ashley Richards concedes a Penalty for a foul on Kerim Frei.
Kerim Frei takes a shot. Michel Vorm makes a save.
Scott Sinclair has a direct shot on goal from the free kick.
Booking Booking for Philippe Senderos.
Foul by Philippe Senderos on Scott Sinclair, free kick awarded.
Danny Graham takes a shot. Save by Mark Schwarzer. Mark Gower produces a right-footed shot from close range which goes wide of the right-hand post.
Substitution Carlos Orlando Sa on for Simon Davies.
Substitution Kerim Frei is brought on as a substitute for Moussa Dembele.
Substitution (Swansea) makes a substitution, with Danny Graham coming on for Leroy Lita.
Shot from just outside the area by Moussa Dembele misses to the left of the target.
Clint Dempsey has an effort at goal from just inside the box that misses to the right of the target.
Kemy Agustien has an effort at goal from the just inside the box hitting the post.
Free kick taken by Michel Vorm.
Substitution Kemy Agustien replaces Luke Moore.
Andrew Johnson takes a shot. Save by Michel Vorm. Outswinging corner taken right-footed by Bryan Ruiz from the right by-line. John Arne Riise is adjudged to have handled the ball.
Clint Dempsey fouled by Mark Gower, the ref awards a free kick. Direct strike on goal from the free kick comes in from John Arne Riise.
Clint Dempsey takes a shot. Save by Michel Vorm.
Free kick awarded for a foul by Steven Caulker on Clint Dempsey. Free kick taken by Simon Davies. Effort by Andrew Johnson from a long way out goes over the target.
Unfair challenge on Brede Hangeland by Leroy Lita results in a free kick. Brede Hangeland takes the free kick.
Bryan Ruiz takes a shot. Save by Michel Vorm.
The assist for the goal came from Wayne Routledge.
55:58 Goal scored
Goal! - Scott Sinclair - Swansea 1 - 0 Fulham Scott Sinclair finds the back of the net with a goal from deep inside the penalty box low into the middle of the goal. Swansea 1-0 Fulham.
Outswinging corner taken right-footed by Mark Gower from the right by-line, save by Mark Schwarzer.
Luke Moore takes a shot. Blocked by Brede Hangeland. Mark Gower takes a outswinging corner from the right by-line played to the near post, Effort from deep inside the area by Ashley Williams misses to the left of the target.
Foul by Leroy Lita on Mark Schwarzer, free kick awarded. John Arne Riise takes the free kick.
Leroy Lita has an effort at goal from the edge of the area that misses to the right of the target.
Unfair challenge on Steven Caulker by Moussa Dembele results in a free kick. Ashley Williams restarts play with the free kick.
Simon Davies concedes a free kick for a foul on Scott Sinclair. Neil Taylor takes the direct free kick.
The referee blows his whistle to start the second half.
45:00 +1:05 Half time
Half Time The ref blows to signal half-time.
The assistant referee flags for offside against Scott Sinclair. Philippe Senderos takes the free kick.
Corner taken right-footed by Simon Davies, Headed effort from close range by Clint Dempsey goes wide left of the goal.
Corner taken right-footed by Mark Gower, Mark Schwarzer makes a comfortable save.
Wayne Routledge takes a shot. Save made by Mark Schwarzer.
Scott Sinclair takes a shot. Mark Schwarzer makes a save.
Free kick awarded for an unfair challenge on Leon Britton by Simon Davies. Neil Taylor takes the free kick.
Corner taken by Mark Gower from the right by-line, Unfair challenge on John Arne Riise by Leroy Lita results in a free kick. Mark Schwarzer restarts play with the free kick.
Luke Moore takes a shot.
Wayne Routledge is ruled offside. Mark Schwarzer restarts play with the free kick.
Bryan Ruiz fouled by Neil Taylor, the ref awards a free kick. Direct free kick taken by Philippe Senderos.
Header from close range by Ashley Williams misses to the right of the goal.
Short corner taken by Mark Gower.
Unfair challenge on Luke Moore by Dickson Etuhu results in a free kick. Scott Sinclair produces a shot on goal direct from the free kick, blocked by Andrew Johnson.
Foul by Ashley Williams on Andrew Johnson, free kick awarded. Shot on goal comes in from Clint Dempsey from the free kick, blocked by Luke Moore.
Headed effort from close range by Leroy Lita goes wide left of the target.
Luke Moore fouled by Dickson Etuhu, the ref awards a free kick. Mark Gower produces a shot on goal direct from the free kick, Moussa Dembele gets a block in.
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