The visitors were plainly short of confidence and there was only one ten minute spell in the second half when they look vaguely like getting anything out of the match.
Michael Bridges skimmed an effort just wide of the post after connecting with Ian Harte's cross and Robbie Fowler brought a great save from Edwin Van der Sar who clung on to a close-range header at the second attempt.
That was it as far as Leeds were concerned. But Fulham spurned a hatful of chances and they were only denied by the brilliance of Paul Robinson who kept the score down to one.
After just 10 minutes Djetou crashed home a header as he met a corner from Boa Morte to lift Fulham 's confidence and less than 30 seconds later it could have been two.
Goldbaek made space for himself on the edge of the box and let fly with a low shot that whistled past the base of the post.
Steed Malbranque was next to test Robinson with a 24th minute effort that the keeper got a hand to.
But Fulham’s Frenchman should have buried his next chance six minutes later. Boa Morte's shot from eight yards was deflected in to Malbranque's path but he thumped his volley on to the bar with Robinson beaten.
The keeper than pulled off two breath taking saves. He palmed away a Sean Davies header and then somehow recovered to tip Malbranque 's close range effort around a post after Pierre Wome shot proved too hot to handle.
As Leeds visibly wilted in the second half Fulham missed easy opportunities, through Davis, Boa Morte and Malbranque, to double their lead.