Luis Suarez had an effort ruled out for offside before Jay Spearing was sent off for a late challenge on Dembele, and the American popped up with the winner
In a fixture with numerous chances at either end, the American took advantage of a fumble from Pepe Reina with five minutes remaining to prod the ball over the line, and edge Martin Jol's men five points clear of the drop zone.
With Brazilian Lucas Leiva out for the duration of the season, Kenny Dalglish called up Jay Spearing for his first Premier League appearance of the campaign but he only lasted 70 minutes before he was sent off for clattering into Belgian Moussa Dembele rather late.
The visitors were aiming for the seventh straight away win, which which would have equalled a club record, but were beaten by Fulham thanks to a winning goal by all-time Premier League leading goalscorer Clint Dempsey.
Moussa Dembele had the game's first chance. Striker Bryan Ruiz slotted the Belgian through but Pepe Reina made himself big to block his shot.
Moments later, Luis Suarez cut back for striker partner Andy Carroll but his powered effort on the stretch was straight at Mark Schwarzer. Then, Charlie Adam’s shot from range was deflected goalbound but the Australian goalkeeper had it covered at his near post.
Clint Dempsey drove at Reina again and this time his shot almost deceived the Spaniard as it swerved mid-air, and the stand-in captain had to palm the ball away.
Into the second half, and the chances kept coming for both sides. Jose Enrique volleyed from outside the box forcing a fine save from Schwarzer.
Liverpool then had the ball in the back of the net; Enrique dinked the ball over the top of the defence and Suarez finished with aplomb, but he was just offside.
The visitors were reduced to 10 men with 20 minutes remaining when Jay Spearing clattered late into Moussa Dembele and his follow through took most of the Belgian with him.The hosts should have taken the lead almost immediately. Fulham’s clever build-up involved substitute Andy Johnson and Dembele, before Ruiz’s pass ended with Dempsey swerving a shot on goal that cannoned back off the bar.
Shortly after, Dembele shot straight at the Spaniard, then drove just wide, as the Cottagers tried to make their man advantage count.
At the other end, substitute Stewart Downing fended off numerous defenders before unleashing a strike that hit the post via a world class save from Schwarzer.
But the deadlock was eventually broken with five minutes left. Danny Murphy’s drive was dropped into the path of Dempsey by Reina, and he slotted past the normally reliable goalkeeper to allow Fulham to hold on for their second home win of the game.