Swansea took the lead through an Aaron Hughes own goal early in the second half.
"Well, a win is always important," Swansea manager Michael Laudrup said.
"It was a great away win after what happened in the last game [against Stoke], when we should have won only for two points to fly away in the last second.
"We knew that Fulham would be very difficult opponents today. They have lost some games recently but they had a chance to beat us today and go above us and away from the relegation zone.
"All these things together made it a very, very, very important game for both of us.
"Us being away added little more difficulty, so apart from the win, the performance over the last 20 minutes of the first half and the whole second was excellent.
"We continued maintaining our style of possession, even in a moment where you could say maybe we should go a little more direct, more simple. We still kept doing what we always do and I think it was a great performance.
"When they scored, we had to go back but we still dominated the rest of the half, except the last four or five minutes like always.
"We got a great second goal and in the end the win, so I really have to say I am very, very pleased with the win and the performance."
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