The Black Cats have struggled in the early stages of the Premier League season and, despite three deserved points, are still languishing down in 15th after 11 games.
Their performance at Craven Cottage belied their position, as record signing Fletcher scored to set them on their way to a routine victory over the 10-man hosts that will ease the pressure on manager Martin O'Neill.
Fletcher, 25, said: "I think this win has been coming, we were unlucky at Everton and it was great to put in a good performance, score a few goals and get three points.
"We saw against Newcastle that it can be tough to play against 10 men but we took the game by the scruff of the neck and got our goals.
"It was an early ball in from Adam (Johnson - for the goal) and a great ball too. When I received the ball and took my first touch I knew I wanted to put it in the far corner and fortunately I managed to do that."
Fulham manager Martin Jol was less pleased in the wake of the game - complaining that the red card issued to towering defender Brede Hangeland was a harsh one.