A goal in each half from Danny Graham and Jonathan De Guzman put the Swans in control, although a nervy finish was ensured when Bryan Ruiz halved the deficit just before the hour.
Fulham piled men forward as the half wore on in search of a second goal, but the Welsh side held on for their first win in five games.
Laudrup was delighted with the way his side doggedly held firm in the face of Fulham's frantic late onslaught.
"It was a difficult game, the first half was OK but in the second half we were under a lot of pressure. But we won the game, it was a great game to win," he told Sky Sports.
"We've won games where we played very well but today it was more our fight.
"Our passing was not that good today, we have to admit that. But we won, we won an away game which is fantastic.
"I think it was good we had fresh legs in there to run and that helped us. In the end they tried the long ball to Brede Hangeland, Dimitar Berbatov and company but we held on to a great result."