Luis Suarez had an effort ruled out for offside and the midfielder was sent off before the American popped up with a winner in the closing stages after Pepe Reina fumbled
With Lucas Leiva out for the rest of the season, Kenny Dalglish handed Jay Spearing his first Premier League appearance of the campaign, but it only lasted 70 minutes as he was sent off by referee Kevin Friend for clattering into Moussa Dembele.
The visitors were aiming for the seventh straight away win, which which would have equalled a club record, but were beaten by the hosts thanks to a winning goal by Clint Dempsey.
Dembele had the game's first chance when Bryan Ruiz slotted the Belgian through but Pepe Reina made himself big to block the shot. A goal would have capped a fine flowing move and directly from that save, the ball was almost in at the other end and Craig Bellamy’s cross saw Charlie Adam instinctively volley goalwards but his effort was blocked.
Moments later, Luis Suarez cut back for strike partner Andy Carroll but his powered effort on the stretch was straight at Mark Schwarzer and Adam’s shot from distance was deflected goalbound but the Australian goalkeeper had it covered at his near post.
Suarez had a shot from range after Carroll’s clever header down to him but his attempt sailed over the bar before Dembele rifled a left-footed drive from outside the box after he made the space for himself and Reina had to be smart to get down quickly and stop the effort falling inside the far corner.
The next big chance came for the Reds when Jordan Henderson’s drove into the box and saw his dinked effort come back off the inside of the post before being cleared away - the 11th time this season they have hit the woodwork in the league.
At the other end, Dempsey drove at Reina again and this time his shot almost deceived the Spaniard as it swerved in mid-air and the stand-in captain had to palm the ball away whilst diving the other way.
Feisty encounter | Luis Suarez was never far from controversy at Craven Cottage
After the break, an overreaction from Dempsey after Bellamy’s tackle saw the American follow the Welshman around with his with his head dangerously close to the Welshman's, resulting in the referee deciding to book the pair of them.
Jose Enrique volleyed from outside the box and forced a fine save from Schwarzer, the shot stopper parrying it away from goal.Liverpool continued to press forcing corner after corner and Suarez again went on a darting run to the byline. He nipped the ball around Brede Hangeland before running into traffic in the box. The referee gave a free-kick to Fulham but could have easily have given a penalty as the Uruguayan appeared to be blocked off.
Friend again was in the middle of controversy after Adam went on a trailblazing, counter-attacking run. He had options either side of him but continued with the ball and was bundled over by Philippe Senderos inches outside of the penalty are and the referee correctly gave a free-kick. Bellamy thundered the resulting set-piece into the wall and out for a corner, from which Daniel Agger headed wide.
Then, Glen Johnson fed Bellamy through with a well-weighted ball through the defence but the striker drove straight across the face of goal and off-target. Liverpool had the ball in the back of the net shortly after when Enrique dinked the ball over the top of the defence and Suarez finished with aplomb but he was ruled just offside in a marginal call.
The visitors were reduced to 10 men with 20 minutes remaining when Spearing clattered into Dembele and his follow through took most of the Belgian with him with his studs raised, although he had initially taken the ball.The hosts should have taken the lead almost immediately after being handed a numerical advantage. Fulham’s clever build-up involved substitute Andy Johnson laying it off, with Ruiz’s pass eventually finding Dempsey, who shot against the bar and was proving to be a thorn in the visitors' side.
Dembele then shot straight at the Spaniard, and again drove just wide, as the Cottagers sensed a potential victory. However, away substitute Stewart Downing fended off numerous defenders before unleashing a chance that hit the post via a world-class save from Schwarzer as Liverpool almost took the points.
But the deadlock was eventually broken when Murphy’s drive was fumbled into the path of Dempsey by Reina and he slotted past the normally reliable goalkeeper from close-range before Fulham held on to secure their second home win of the season.
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