Having gone into the game hoping to bounce back from 5-1 and 6-1 home defeats to Crystal Palace and Liverpool respectively, Leeds were unable to impose themselves as they fell to a 2-1 loss.
After a lacklustre first half at Craven Cottage, Fulham found the breakthrough with Harry Wilson continuing his return to form with a second goal in as many games with a well-timed 58th-minute volley.
Andreas Pereira doubled Fulham's lead after Illan Meslier came for a cross but was unable to clear, with the ball falling for the unmarked 27-year-old just five yards out.
Leeds pulled one back with 11 minutes to go to inject life into their performance, as Patrick Bamford's effort was deflected into the back of the net off Joao Palhinha.
The visitors tried to push for an equaliser but, despite a significantly improved performance than in the previous 80 minutes, they were unable to level the game.
Fulham gave away a few needless fouls in the early part of the match, including one just outside the box, which almost led to Leeds' opener.
Marc Roca curled the ball towards the far corner, with Bernd Leno making his first save of the match.
The first half lacked intensity, despite Leeds' perilous position and the fact they conceded 11 goals in their last two matches.
Chances were limited throughout the opening period with Pereira resorting to trying his luck from distance just before the break, but his drive was straight at Meslier.
There was a slight increase in pace at the start of the second half, with Willian firing just wide for Fulham in the 49th minute.
After a slightly lacklustre performance, Fulham found the breakthrough in the 58th minute.
Antonee Robinson drove down the middle, before playing in Willian down the left. The Brazilian's cross was tipped straight into the path of Wilson who volleyed home.
The goal sparked the Cottagers into life as they looked to inflict further misery on Leeds, with Pereira's direct free-kick rebounding off the crossbar just after the hour mark.
Fulham doubled their lead in the 71st minute. Pereira started the move before Robinson's cross was not dealt with by Meslier, and no one was picking up the Brazil international who fired into the back of an empty net from five yards.
Leeds pulled one back to set up an exciting finish to the encounter when Bamford's flick at the far post was deflected into his own net by Palhinha.
Despite eight minutes added on, Fulham - who also beat Leeds 2-0 in the FA Cup fifth round in February - secured a Premier League double over the struggling Whites.