Martin O'Neill's side had not won since September 29 when Fletcher's goal secured a 1-0 victory over Wigan.
Scotland international Fletcher had not scored since claiming the winner against the Latics until he opened the scoring at Craven Cottage early in the second half.
Fulham were already down to 10 men following Brede Hangeland's first-half dismissal but levelled through substitute Mladen Petric.
But Sunderland fought back with goals from Carlos Cuellar and Stephane Sessegnon to win their first Barclays Premier League away game of the season and Fletcher claims it was deserved.
"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," he said.
Sunderland failed to make a numerical advantage count in last month's derby clash with Newcastle but Fletcher, who also praised the performance of winger Adam Johnson, felt they handled Fulham's 10 men better.
He said: "We saw against Newcastle that it can be tough to play against 10 men but today [Sunday] we took the game by the scruff of the neck and got our goals.
"It was an early ball in from Adam (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."
Meanwhile, Fulham substitute Mladen Petric says they have to learn from their defeat.
Goalscorer Petric had an incident-filled game after replacing the injured Bryan Ruiz after an hour.
The Croatia international almost equalised with his first touch before finding the back of the net two minutes later after Damien Duff beat the offside trap to provide the assist.
Petric then required treatment on a wound suffered when scoring the goal and was off the field as Sunderland regained the lead.
"It was a hard game for us because it started very badly with the red card for Brede," Petric said.
"Then we were 1-0 down so it was good to come back and equalise, although they scored two minutes after my goal which was a pity.
"I got a kick on my calf when I scored," Petric said.
"It made a cut so I had to come off to have stitches put in and then by the time I got back on the pitch it was 2-1. It was a bit painful but I had injections so it was okay."
Petric managed to see out the rest of the game and was denied a second goal by a great save from Sunderland goalkeeper Simon Mignolet.
But Fulham boss Martin Jol lost both Alex Kacaniklic and Ruiz to hamstring injures and Petric felt the enforced changes had an impact of the Cottagers' chances.
"I think we have to learn from that game, but we had two injuries so I think that luck was not on our side," he said.
"I think we tried very hard and we always believed we had it in us to get back in the game.
"We kept putting pressure on Sunderland and we had some good opportunities again to score but unfortunately we just couldn't find the net again."
Jol's side travel to Stoke next weekend with Hangeland, Kacaniklic and Ruiz all missing but it is the absence of the club's captain that worries Petric most.
"Of course it will be a difficult game when we go to Stoke at the weekend," he said.
"It will be especially difficult because Brede is suspended and it is the kind of game you need your big centre-back because he's a tall player and he's very strong with his head."