Fulham created plenty of chances to improve their perilous league position but ended the match with 10 men as Leeds ultimately eased to victory.
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The hosts made the brighter start to the match and could have taken the lead inside six minutes when former Leeds pair Matt Smith and Ross McCormack linked up, only for the latter to be denied by Marco Silvestri.
Bryan Ruiz and Konstantinos Stafylidis both drew further saves from the visiting keeper inside the opening 10 minutes, with the former's chip being tipped over and the latter's strike helped round the post.
Fulham continued to apply the pressure and Smith was the next to be denied by Silvestri, whose crossbar came to the rescue from the resulting corner as Ruiz's delivery hit the woodwork.
Smith's aerial threat continued to cause his former side problems and he came within a whisker of breaking the deadlock in the 18th minute, only to see his header drift narrowly wide.
Leeds registered their first effort midway through the first half when Giuseppe Bellusci's speculative long-range effort was comfortably saved, but having withstood the heavy early pressure it was the visitors who opened the scoring.
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Things went from bad to worse for the Cottagers shortly afterwards as Stafylidis picked up a second yellow card for a late challenge just a minute after being booked for dissent.
The red card seemed to galvanise the hosts, however, and Silvestri was forced to come to the rescue to deny both Ryan Tunnicliffe and Smith before the hour mark.
The Leeds keeper was beaten shortly afterwards, but once again had the woodwork to thank as Michael Turner's header struck the post.
Smith had two more decent chances in the final 20 minutes, but the visitors killed the game off once and for all two minutes from time as Mirco Antenucci converted a rebound after Marcus Bettinelli had saved Byram's initial effort.