Darren Bent climbed off the bench to fire Fulham to their first home win in almost six months in an all-Premier League clash at a wet and windy Craven Cottage.
Everton looked set to ease in to the fourth round of the Capital One Cup after dominating the first half and they took a well-deserved lead in the 12th minute when Steven Naismith tucked away a fine ball from Gerard Deulofeu.
Martin Jol's side had lost five and drawn one of their previous six home games, but Dimitar Berbatov levelled with his first of the season before Bent wrapped up the win in front of England manager Roy Hodgson, less than three minutes after his introduction from the bench.
Fulham goalkeeper David Stockdale was called into action early, making a fine save from Naismith, but the midfielder made no mistake soon after.
Played onside by Scott Parker, Naismith latched on to a wonderful throughball from Deulofeu before driving the ball between David Stockdale's legs.
Sylvain Distin hit a post as Everton continued to apply the pressure, and then the Deulofeu show began in earnest.
The Barcelona loanee beat three Fulham players inside the home box and only a desperate block from Brede Hangeland denied the winger a goal.
The bodies of Fulham defenders bounced off Romelu Lukaku as he strode towards goal but the strength of his shot did not match that of his run.
Deulofeu could have doubled their lead when smacked a low drive just wide of Stockdale's goal just before the break.
However, Fulham returned from the break rejuvenated after being booed off at half-time with Alex Kacaniklic went close with a stinging drive and Pajtim Kasami finally started coming in to the game.
Fulham's equaliser came nine minutes into the second half as Seamus Coleman accidentally diverted Pasami's pass in to Berbatov's path when he tackled Taarabt and the Bulgarian tucked the ball away.
Everton looked rattled and Jol sought to take advantage by throwing Bent on and it proved to be an inspired move.
The England international made an immediate impact, scoring Fulham's second in a move directly exported from the Fulham training ground, with Hodgson watching on in admiration from the stands.
Giorgos Karagounis shaped up to shoot at goal from 30 yards, but instead he rolled the ball off to an unmarked Bent and he rifled the ball beyond Robles from a tight angle.
Fulham fans held their breath as Lukaku's low drive almost squirmed between Stockdale's legs before the keeper was forced to save again with his legs from Coleman in a frenetic last few minutes.
The Fulham faithful who chanted "Jol out" 10 days ago cheered the Dutchman and his men off the field after a welcome win for the west London club.
Roberto Martinez, on the other hand, will travel back up to Merseyside not knowing how his team failed to win after dominating the first half.