Carson, whose blunder against Croatia contributed to England failing to qualify for Euro 2008, got both hands to Simon Davies' 30-yard drive on the brink of half-time but could only deflect the ball into his own net.
West Brom's 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.
Kamara was given his chance against his former club after Johnson was ruled out with a tight hamstring and he almost blasted Fulham ahead in the opening minutes after a brilliant piece of control in the box.
The Senegal striker pulled Chris Baird's long ball out of the air with a deft touch and turned to fire a low shot, which Scott Carson did well to block.
Kamara worked space for himself again on the edge of the box but Gonzalo Jara nipped in to steal the ball before he could get a shot away.
West Brom striker Peter Odemwingie forced Stockdale into action, first to block a driven cross and then to stop a low deflected shot from the edge of the box.
But Fulham were on top of a lively encounter and the visitors' new-look defence was struggling to contain Kamara, who cut inside Gianni Zuiverloon and laid the ball off for Clint Dempsey.
The American went to ground in the box under a challenge from Youssuf Mulumbu but referee Martin Atkinson waved away Fulham's vociferous penalty appeals.
At the other end, Odemwingie 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, Fulham launched a throw into the West Brom box. Dempsey did well to ride two challenges and bring the ball down but his shot was blocked.
The change at the back did nothing to settle West Brom's defensive nerves.
Hurst failed to deal with Pantsil's long cross, allowing the ball to fall into the path of Simon Davies, 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.
Brede Hangeland climbed storeys above Carson and the West Brom defence to meet Davies' corner but he planted his powerful head just wide - moment before taking the goalkeeper's attempted punch full in the face.
Indeed, Carson made better contact with Hangeland's face than he did to Davies' swerving shot that put Fulham ahead in first-half stoppage time.
Mulumbu was robbed of possession by Dickson Etuhu, who teed up Davies for a 30-yard drive which Carson deflected into his own net.
Davies' strike gave Fulham real impetus and Duff went within inches of doubling their lead seven minutes after the interval 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 wing and then delivered the cross to the edge of the six-yard box, where Dempsey planted his header firmly past Carson.
Dempsey did well to keep his eye on the ball as it flashed past Hangeland's towering leap.
The next time Hangeland launched himself at a Davies corner, just nine minutes later, his timing and his aim were perfect.
It was not as if West Brom had not been warned but no-one picked up Hangeland's late run and, at the third time of asking, he met Davies' corner to beat Carson from six yards.
Dejected West Brom had nothing left to offer. Fulham saw out the remaining minutes comfortably and could well have scored a fourth goal.
Etuhu moved in from the left and unleashed a fierce drive from the angle of the penalty area which whistled just over Carson's bar.