The Swans demonstrated they could not only win without injured top scorer Michu, but also grind out a result.
Danny Graham and Jonathan de Guzman put them 2-0 up, thanks to a little help from Fulham goalkeeper David Stockdale, before Brian Ruiz pulled one back.
Laudrup said: "You can't always win playing well with the ball. That's what I talked about when I arrived some months ago, that sometimes you have to use a Plan B or Plan C.
"Because, if you always want to do the same thing, if that's not working, do we just stop playing our game or go home or what?
"I think it was a great win and once more showed that our team has character."
Laudrup hailed Graham, who filled the void left by Michu with his first league goal in four months.
"It was so important for him to score that goal," he said, reiterating he would sit down with Graham next month and hinting he would consider allowing him to leave if he wanted more guaranteed game time.
He also said Michu could be fit for Tuesday's game with Aston Villa.