Scott Carson made another high-profile mistake on the stroke of half-time to set Mark Hughes' men on course for victory.
Carson, whose blunder against Croatia contributed to England failing to qualify for Euro 2008, got both hands to Simon Davies' 30-yard drive on 45 but could only deflect the ball into his own net.
West Brom's new-look defence was then exposed after the break as Fulham cruised to a first home win in six attempts with headed goals from Clint Dempsey and Brede Hangeland.
While Fulham climbed above West Brom into 13th place to relieve some of the pressure on Hughes, the Baggies' slump continued.
A fifth consecutive defeat represented their worst run in six years and having been eighth before Christmas they now hover just two points above the relegation zone.
Manager Roberto Di Matteo welcomed Gonzalo Jara back from suspension while James Hurst and Gianni Zuiverloon also came into the back four.
Fulham were without goalkeeper Mark Schwarzer, who was away on international duty, and injured striker Andrew Johnson but that gave Diomansy Kamara a chance against his old club.
The Senegal striker almost blasted Fulham ahead in the opening minutes after a brilliant piece of control in the box.
Kamara pulled Chris Baird's long ball out of the air with a deft touch and turned to fire a low shot, which Carson did well to block.
West Brom had their moments in the first half and striker Peter Odemwingie forced Fulham keeper David Stockdale into action with a low deflected shot from the edge of the box.
But Fulham were on top of a lively encounter and the visitors' defence was struggling to contain Kamara, who cut inside Zuiverloon and laid the ball off for Dempsey.
The American went to ground in the box under a challenge from Youssuf Mulumbu but referee Martin Atkinson waved away Fulham's penalty appeals.
At the other end, Jerome Thomas escaped the Fulham defence with an angled run but his shot went straight at Stockdale and John Pantsil, whose mistake had led to the chance, cleared with an overhead kick.
Marek Cech went down injured after a challenge from Pantsil and had to be replaced by Nicky Shorey after half an hour.
While the Slovakian was off receiving treatment, Dempsey did well to ride two challenges and bring the ball down in the box but his shot was blocked.
West Brom's nervous defensive display continued. Hurst failed to deal with Pantsil's long cross, allowing the ball to fall into Davies' path but the Welsh midfielder's volley fizzed across goal and wide.
Damien Duff's deflected shot forced Carson to scramble after another poor West Brom clearance and from the subsequent corner Fulham should have taken the lead.
Hangeland climbed above Carson and the West Brom defence to meet Davies' corner but he planted his powerful head just wide - moments before taking the goalkeeper's attempted punch full in the face.
However, Davies' swerving shot put Fulham ahead in first-half stoppage time.
Mulumbu was controversially robbed of possession by Dickson Etuhu, who teed up Davies for a 25-yard drive which Carson deflected into his own net.
Davies' strike gave Fulham a real impetus and Duff came within inches of doubling their lead seven minutes into the second half when he was allowed to turn on the edge of the West Brom box.
Carson was relieved to see his low shot across goal skid just wide - but the feeling was only temporary.
Davies won Fulham a corner with a determined run down the left and then delivered the cross to the edge of the six-yard box where Dempsey planted his header past Carson.
Dempsey did well to keep his eye on the ball as it flashed past Hangeland's towering leap. A second warning about the Norwegian's aerial prowess that went unheeded.
And the next time Hangeland launched himself at a Davies corner, just nine minutes later, his timing and his aim were perfect.
No-one picked up Hangeland's late run and, at the third time of asking, he sailed through the air to meet Davies' corner to beat Carson with a powerful header from six yards.