Defenders Philipp Degen and Jamie Carragher were two of eight players to be dismissed in total as Rafa Benitez's side went down to their fifth league defeat of the season.
Chelsea remained top by two points with a comfortable 4-0 win at 10-man Bolton Wanderers, while Manchester United stayed in touch with a 2-0 victory over Blackburn Rovers.
Third-placed Arsenal won 3-0 against north London rivals Tottenham Hotspur, who are fourth, thanks to a Robin van Persie double either side of Cesc Fabregas's brilliant solo effort.
The win puts Arsene Wenger's men on 22 points, five behind London rivals Chelsea with a game in hand.
Erik Nevland restored Fulham's lead after 73 minutes before Degen and Carragher received straight red cards within three minutes of each other and Clint Dempsey added a third goal to move Fulham up to 11th.
"We were able to keep our noses in front and anytime you take a scalp the size of Liverpool's you have got to be happy," Fulham manager Roy Hodgson told Sky Sports News.
"I don't think people will begrudge us the victory because I thought we were worth it over the 90 minutes.
Liverpool manager Rafa Benitez begged to differ, saying: "Always it's hard to take any defeat but especially this one because we were in control of the game."
"It's a question of taking your chances when you create them and don't make massive mistakes like today and give a lift to the other team."
DINDANE MASTERCLASS
Deco added a second on the hour before a Zat Knight own goal and a Drogba strike completed the rout for Carlo Ancelotti's team.
Dimitar Berbatov's smart turn and volley provided the highlight of an otherwise laboured United performance as Alex Ferguson's side beat struggling Rovers at Old Trafford.
