"I'm just delighted. I thought they were brilliant and it couldn't have come at a better time," Coleman said after the game at Craven Cottage.
"Three points against anyone would have been sweet but against Chelsea, the champions, in a local derby was sweet.
"Some ridiculous stories have been printed about me this week and that makes people nervous and ask questions about my future.
"The chairman has been 100 per cent supportive about my future and the players have kept together and we've come out and shut people up by getting three points."