The Reds' outstanding form on the road ended during a controversial evening in west London.
Dempsey stabbed home after a long-range 85th-minute shot by Danny Murphy bounced off the arms of Pepe Reina, thus securing only Fulham's third league win of the season.
However, a sense of grievance cloaked Liverpool's night after they were denied a strong claim to a penalty and a legitimate goal from Luis Suarez was disallowed for offside, before Jay Spearing was shown a straight red card.
Philippe Senderos hacked down Charlie Adam with referee Kevin Friend claiming the tackle was executed just outside the area in what was a desperately tight call.
Worse was to come when Suarez produced a brilliant finish after jinking his way clear, only for a flag to be raised even though the Uruguay striker was onside.
The final insult was delivered in the 72nd minute when Spearing, making his first Premier League start of the season, was shown a straight red card.
Spearing, who had replaced knee-injury victim Lucas Leiva in the starting line-up, caught Moussa Dembele with a sliding challenge, but only after cleanly winning the ball in what was a harsh call.
The result denied Liverpool a record-equalling seventh successive away win in all competitions as they endured their first defeat in 12 games.
They dominated long spells of the game yet their defence was unpicked with five minutes gone, Bryan Ruiz finding Dembele with a wonderful through-ball.
Dembele was through on goal but his first touch was disappointing, giving Reina the time to close down the space.
The lively start continued when Suarez picked out Andy Carroll only for the England striker to stab his shot straight at Mark Schwarzer.
Schwarzer was then forced to dive to his right to deny Adam following some inventive build-up play from Liverpool.
It was then Reina's turn to scramble across goal as Dembele directed a fine effort towards the bottom-left corner, and moments later Dempsey tested the Spaniard.
Liverpool were the more incisive side going forward, though they could ill-afford any lapses in concentration with Fulham showing flourishes in attack.
Jordan Henderson struck the right post having expertly glided his way into a shooting position and shortly after, he combined with Carroll to set up a chance for Suarez that crept wide.
On two occasions, Dempsey tried his luck from just outside the area, but Reina was alert to one while the second struck the advertising boards.
Suarez was hacked down on the edge of the area but Adam's kick was easily dealt with by Senderos.
Bellamy brought down Dempsey, resulting in a face-off between the two with Fulham's American forward the aggressor, though Friend booked both players.
Jose Enrique fired a dangerous shot that Schwarzer did well to palm clear of danger as Liverpool controlled the early exchanges of the second half.
Fulham were lucky to escape a penalty in the 59th minute when Senderos brought down Adam.
The initial tackle appeared to have been made just outside the line, but contact continued well inside the area.
Friend was well positioned and refused to award a penalty with Bellamy hitting the free-kick into the wall.
Carroll, Liverpool's £35million signing from Newcastle, saw a shot head towards the corner flag and was taunted with chants of "what a waste of money".
Suarez had his goal disallowed and Liverpool's frustration boiled over in the 72nd minute when Spearing was sent off for his challenge on Dembele.
Dembele had the bit between his teeth as Fulham pushed for the winner, going close on two occasions.
At the other end, substitute Stewart Downing saw Schwarzer superbly tip his shot onto the post as a frantic climax beckoned.
The killer blow landed with six minutes of normal time remaining, starting with Murphy pulling the trigger from well outside the area.
Reina failed to control the ball and the lurking Dempsey was able to convert from close range.
The win moves Fulham up to 13th spot, five points clear of the drop zone - the same margin that separates seventh-placed Liverpool from Chelsea, who currently occupy the final Champions League qualifying position.