Dempsey prodded home on 85 minutes after Pepe Reina had turned away Danny Murphy's shot.
It had been a real ding-dong battle that saw shot after shot pepper both goals — yet with no result.
But Jay Spearing's 72nd-minute red card, for scything through Moussa Dembele, gave Fulham the advantage — before Dempsey cashed in by grabbing the points.
It had taken just five minutes for the first chance to be carved out.
Moussa Dembele and Bryan Ruiz sliced their way through — only for the Belgian to hit his shot straight at Pepe Reina.
At the other end, Andy Carroll had a sighter but Mark Schwarzer saved his shot.
Charlie Adam was next the threaten and pinged a shot at the Fulham stopper.
It was end-to-end stuff already and Dembele and Dempsey both tested Reina with sharp long-rangers.
Liverpool were a whisker from taking the lead after Jordan Henderson's dazzling 27th-minute run.
Henderson danced through Fulham before dinking a shot against the post.
Reina was called into action again when Dempsey hit a wobbler from distance.
Incredibly, though, neither team could find a way through and the half ended goalless.
After the break, both sides came charging out of the blocks — and Schwarzer pulled off a cracking early save from Jose Enrique.
Liverpool then threatened as it pinballed around the box but Fulham held firm.
Luis Suarez was then shouting for a penalty after going down between Brede Hangeland and John Arne Riise.
Yet the striker's reputation went before him and his claims were dismissed.
The Reds had a much more convincing appeal when Charlie Adam's darting run was ended by Phillipe Senderos.
Senderos hauled down the Scot on the edge — and got the benefit of the doubt when a free-kick was given.
Bellamy drilled the set-piece wide and it was a real let-off for the Cottagers.
The Wales man was in the thick of it again shortly after when he dragged Glen Johnson's through-ball wide.
Fulham were under the cosh now — yet were handed a boost when Spearing saw red for scything through Dembele on 72 minutes.
The Kop ace dived in with both feet off the air and was sent for an early bath.
Dempsey hit the bar with 10 minutes to go — and Downing had his own brush with glory when Schwarzer tipped his shot onto the post.
Incredibly, there was still time for more drama.
Murphy skinned Glen Johnson on the left before taking a pot-shot at goal. That was saved by Reina, but Dempsey was on hand to turn in.
DREAM TEAM RATINGS
STAR MAN - MOUSSA DEMBELE
FULHAM: Schwarzer 7, Kelly 7, Hangeland 8, Senderos 7, Riise 7, Dempsey 7, Murphy 7, Etuhu 7, Dempsey 7, Dembele 8, Ruiz 7, Zamora 6. Subs: Johnson (Zamora 71) 5, Gecov (Murphy 90) 5. Not used: Etheridge, Hughes, Briggs, Kasami, Frei. Booked: Dembele, Senderos, Dempsey.
LIVERPOOL: Reina 6, Johnson 7, Skrtel 7, Agger 7, Enrique 7, Henderson 7, Spearing 7, Adam 8, Bellamy 7, Suarez 7, Carroll 6. Subs: Kuyt (Carroll 77) 5, Downing (Bellamy 77) 5. Not used: Doni, Coates, Carragher, Kelly, Maxi. Booked: Bellamy. Sent off: Spearing.
REF: K Friend 5
Out of order: Liverpool's Luis Suarez made a gesture to Fulham fans
Luis Suarez - who is already facing a racism charge - could find himself in more hot water with the FA after making an obscene gesture towards Fulham supporters after Liverpool's 1-0 defeat.
The Anfield striker was given a torrid time by the home support throughout the clash at Craven Cottage as he was subjected to chants of 'cheat' for what Fulham supporters perceived to be his constant diving.
And Suarez cracked after the final whistle by making an explicit hand gesture towards Cottagers fans. Wembley disciplinary chiefs will decide on Tuesday whether to investigate the incident further.
Suarez has already been charged by the FA for making racist remarks towards Manchester United defender Patrice Evra during the 1-1 draw at Anfield earlier this season.
And Reds manager Kenny Dalglish admitted he could be forced to talk to Suarez about his conduct after the latest controversy to hit the Uruguay international.
'I haven't seen the picture and I'm not taking anybody's word for it,' said Dalglish.
'If you show me the picture and I'm convinced that what you're saying is true, then I've got a decision to make.'
In response to Fulham fans branding Suarez a 'cheat', Dalglish added: 'That's scandalous. We'll look after Luis as best we can, and I think it's about time he got a bit of protection from some people.
Lunge: Jay Spearing fouls Fulham's Moussa Dembele before being sent off
'His integrity is impeccable. He can look in the mirror and go to bed at night and sleep soundly.'
Liverpool's misery was compounded by Jay Spearing's debatable sending off - the latest incident in a controversial weekend of refereeing decisions.
The Liverpool midfielder clearly made contact with the ball in his challenge with Moussa Dembele - but was given his marching orders by Kevin Friend after catching the Fulham forward with his follow through.
And Dalglish felt his midfielder was harshly sent off: 'I think, you need to ask the referee what their interpretation is? What the level of acceptance is? 'Jay never had another thought in his mind but to win the ball, and he did win it.
Turning point: Spearing is sent off as Liverpool's players protest
'As long as the officials are consistent, it's not a problem. But I don't think we were going to get anything tonight, were we?
'The (offside) goal that Luis scored, Charlie [Adam] could have had a penalty. We played well enough to have won the game.'
Fulham boss Martin Jol added: 'Was it a red card? I think it was a bad tackle. 'If you see from another angle, you saw his ankle up there and I think it was a sending off.'
One step forward, Two steps backward.
Back to drawing board again.
A defeat is a defeat and they need to re-group again.
no lucas .. no win
actually suarez has a goal disallowed, but he onside
Kenny decided to play his team B against Fulham and they lost.
Maybe they over-estimated themselves and forget that they still have to play hard to win.
Did not watch the match but the feedback that I gathered from the forums is that the whole team did not play well.
Kenny will need to buy more players and play Carroll in the reserves until he find his scoring touch and sense like RVP.
i wonder if carroll and torres meet to exchange ideas on how to recover their scoring touch.
ask carroll go chelsea
torres come back liverpool
in liverpool , when torres has the ball he ethier pass or juz shoot directly
but at chelsea once he had the ball , he wan to shoot also no place to shoot , then had to pass
Henderson, Downing, Caroll playing.
Took up 3 spots on the team.
Everytime Caroll plays, I drop my odds for a liverpool win by 50%.
Liverpool is already playing with 10 men when Carroll is fielded.
Kenny must be scared that some of key players will be injured like Lucas.
His UK pets just dun make the standard at the moment.
Even Kuyt also lost his standard.
Their sudden up and down is making money for Sg Pools.
Originally posted by Medicated Oil:Liverpool is already playing with 10 men when Carroll is fielded.
Kenny must be scared that some of key players will be injured like Lucas.
His UK pets just dun make the standard at the moment.
Even Kuyt also lost his standard.
Their sudden up and down is making money for Sg Pools.
Even you noticed it everytime Caroll plays?
Until Caroll starts scoring, not just plays better, will I change my opinion of him.
they should loan torres back
Lost.... haiz... me too.. haiz...
Although Crouch did not score for Liverpool after 13 matches, he was at least getting the ball and chasing for the ball or providing goal assist.
I may complained about him but I recognised his attempt in getting his goal eventually.
As for Carroll, except for playing hard for a few matches, he is invisible. (He can change his name to John Cena, "You can't see me !!!")
I dun see the value of starting him as he only deserved a place in substitution for time wasting.
Luis did not score all the time but he is working his heart out when he get the ball.
He is a player truly worth millions.
Not really finding a scape goat for the defeat but hope Kenny can recognise that he can only rely on a few men and they are definitely not born in UK.
- mod no do job so i gotta do -
This is liverfool that we all know all along.
Nothing surprising.
They only perform well against big teams.
Originally posted by gunner77:This is liverfool that we all know all along.
Nothing surprising.
They only perform well against big teams.
Can beat Chelsea and hold the 2 Mannies to a draw but cannot beat Swansea, Norwich and Fulham.
They are harder to figure out than gift exchanges during xmas time.
Originally posted by charlize:Can beat Chelsea and hold the 2 Mannies to a draw but cannot beat Swansea, Norwich and Fulham.
They are harder to figure out than gift exchanges during xmas time.
Nothing change for the last 2 decades.
Pool beat Fulham 5-2 in May and when asked if Liverpool could challenge for the title in 2012... Murphy replied: "It's hard to say because they have been playing under very little pressure. They haven't needed to go out and win games, and everything they get now is a bonus. It will be a different ask for those players to play under pressure every week if they are near the top, but with Kenny in charge and a few more additions they will be pushing for the top four again."
Dalglish was unhappy and rebuked Murphy who championed Hodgson's credentials for the Liverpool job. The Liverpool manager said: "He [Murphy] should know there is always pressure here. He played here long enough, didn't he? I just know that we played fantastic that night against Fulham and so does he. (Pool won 2-5).
Looks like Murphy wanted to get one back at Kenny... and did it... lol.
Yeh that murphy line. He's right actually lol.
Some of the players need to buck up.
With Luis sharing the middle finger with the Fulham fans, Ah Ken will have to rely on "John Cena" to create a miracle for Liverpool on the next two matches.
I hope Ah Ken would be able to look deep into his squad to form a winning team.
Liverpool is as unpredictable as ever.
That is why it is the best club to support.
I think liverpool wont finish top 4. city and united will fight it out for the top 2 positions, with chelsea, arsenal, spurs and liverpool all fighting to fiinsh third and fourth place. I choose spurs and arsenal to finish 3rd and fourth respectively.
It's hard to remove a legend lol.