Dempsey stabbed home a long-range 85th-minute shot by Danny Murphy that had bounced off the arms of Jose Reina, to secure only Fulham's third Barclays Premier 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 Mousa Dembele with a sliding challenge, but only after cleanly winning the ball in what was a harsh call.
After Dempsey's strike, Liverpool substitute Stewart Downing hit the post in a frantic climax to the game.