Liverpool were looking comfortable at Craven Cottage, but the game's dimensions changed when Spearing was sent off in the 72nd minute.
The academy graduate was handed a straight red card during an innocuous passage of play, apparently for following through with a kick on Dembele having won the ball cleanly in the tackle.
Spearing's departure saw Fulham attack in numbers and rattle the crossbar with 10 minutes remaining as Dempsey found space on the edge of the box to curl in an effort.
Dembele had a shot parried by Reina as the Cottagers pushed for a winner, before the Belgium international then saw an effort sneak just wide.
Fulham had Schwarzer to thank for tipping substitute Stewart Downing's shot onto the post moments later, before Dempsey fired home the winner at the other end.
Former Liverpool left-back John Arne Riise unleashed a powerful shot that Reina could only palm into the path of Dempsey, who finished from close range to secure the home side three points.
Intro: Clint Dempsey's last-gasp goal earned Fulham victory against 10-man Liverpool this evening.
After an even first period, Liverpool looked rejuvenated and dominated proceedings until Jay Spearing was controversially sent off in the 72nd minute.
The red card swayed the match in Fulham's favour and their pressure paid dividends when Dempsey tucked home from close range five minutes from time after Jose Reina could only parry a shot from John Arne Riise.