The Swans has not won in the league since beating Newcastle United 3-0 on December 4, a streak of eight games without success, but got the win they required thanks to second-half goals from Jonjo Shelvey and Chico Flores.
Shelvey, who had struck the crossbar in the first half, opened the scoring in the 61st minute when his 25-yard attempt deflected devilishly off Brede Hangeland and past a hapless Maarten Stekelenburg.
With 15 minutes remaining, central defender Chico Flores rose above to glance home Jonathan de Guzman's free-kick with his head, via a touch off Dimitar Berbatov, allowing the home side to double their advantage.
Fulham had chances to score in the first half but Ashkan Dejagah and Clint Dempsey were profligate as Rene Meulensteen's men were beaten for the fourth time in their past five league outings to remain just a point clear of the drop zone.
Meanwhile, Michael Laudrup's Swans were able to move up to tenth with their sixth triumph of the campaign taking their points tally to 24 from 23 outings.
2013/14 Barclays Premier League season scores
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