Fulham manager Mark Hughes had been booed after his side's Boxing Day defeat by West Ham United at Craven Cottage but an encouraging away win over Stoke City and a narrow defeat at Tottenham in the meantime had improved the mood.
And it was Hughes's side who came out quickest, flooding forward and putting pressure on the inexperienced West Brom back-line which contained three enforced changes due to injuries.
The first opportunity of the match came when a long ball from Chris Baird found Diomansy Kamara, who controlled on the edge of the six-yard box, swivelled and forced a good save low down from Carson.
But while Fulham dominated possession, they created few clear-cut chances early on and West Brom continually threatened on the counter attack.
Hughes open to new signings
David Stockdale started in goal for the home side for the first time since August with Australian Mark Schwarzer away on Asian Cup duty.
And Fulham had the 25-year-old, who was tipped for an England call up after impressing early in the season, to thank for keeping the score level.
First Stockdale saved from Peter Odemwingie's low snap-shot before a through ball from Chris Brunt split the Fulham defence and found Jerome Thomas who went one-on-one with Stockdale but the keeper stood firm and saved well.
But West Brom's defensive problems got worse on the half hour mark when Marek Cech was caught on the knee by John Pantsil's trailing leg and the Slovakian had to be replaced by Nicky Shorey at left-back.
Suddenly, every set-piece was a great opportunity for Fulham to take advantage of a West Brom defence which had not previously played together.
Di Matteo ready for relegation scrap
And take advantage the Cottagers did. With five minutes to go until half-time, Hangeland should have given Fulham the lead when he rose high to meet Davies's corner but the Norwegian nodded wide of the left post with the goal at his mercy.
Hughes's side eventually took the lead when Davies was benefactor of a goalkeeping blunder, although West Brom had a good claim for a foul in the build up.
Dickson Etuhu appeared to dispossess Youssuf Mulumbu unfairly on the edge of the area but the referee waved play on. The midfielder then rolled the ball to Welshman Davies who unleashed a fierce effort which, while powerful, was straight at Carson, only for him to allow the ball to inexplicably slip through his hands.
We needed three points - Hangeland
Rather than sit back on their lead in the second half, Fulham pushed on for a second goal and almost found one when Damien Duff whistled a right-footed effort wide of the left post.
Minutes later they did double the lead when Dempsey leaped to head his seventh goal of the season from Davies's corner.
And when another Davies corner caused havoc, Hangeland was able to make it three as he ghosted into the box unmarked and headed between the legs of Carson.
The game could have turned into a rout had Fulham kept pushing but a series of substitutions slowed the pace and the home side were happy to play out a convincing victory which leaves them in mid-table and leaves West Brom in freefall after five straight defeats.
90:00+3:08 The referee signals the end of the game.
90:00+1:55 The ball is crossed by Jerome Thomas.
90:00+1:14 Graham Dorrans delivers the ball, Chris Baird manages to make a clearance. Outswinging corner taken right-footed by Graham
Dorrans from the right by-line.
90:00+1:01 Outswinging corner taken right-footed by Graham Dorrans from the right by-line.
90:00+0:51 A cross is delivered by Jerome Thomas, Aaron Hughes makes a clearance.
90:00+0:25 Chris Baird challenges Marc-Antoine Fortune unfairly and gives away a free kick. Graham Dorrans takes the direct free kick.
89:06 Foul by Peter Odemwingie on John Pantsil, free kick awarded. David Stockdale restarts play with the free kick.
89:06 Booking Peter Odemwingie is shown a yellow card.
87:47 Outswinging corner taken by Graham Dorrans from the right by-line, clearance by Aaron Hughes.
87:34 Peter Odemwingie takes a shot. Save by David Stockdale.
86:16 Substitution (Fulham) makes a substitution, with Eddie Johnson coming on for Clinton Dempsey.
86:04 Centre by Nicky Shorey, Dickson Etuhu manages to make a clearance.
85:28 Clinton Dempsey takes a shot. Scott Carson makes a comfortable save.
84:25 Graham Dorrans produces a right-footed shot from just outside the penalty box that goes wide left of the target.
83:56 The ball is swung over by Jerome Thomas.
82:34 Effort on goal by Dickson Etuhu from just inside the area clears the crossbar.
81:20 Substitution Bjorn Helge Riise replaces Simon Davies.
81:02 Chris Brunt has a shot on goal from outside the box which misses right.
79:44 Marc-Antoine Fortune challenges John Pantsil unfairly and gives away a free kick. David Stockdale takes the free kick.
76:43 Free kick awarded for a foul by Gianni Zuiverloon on Clinton Dempsey. Danny Murphy crosses the ball from the free kick right-footed
from right channel, clearance made by Simon Cox.
75:49 The ball is delivered by Nicky Shorey, David Stockdale makes a save.
74:43 Effort from just outside the box by Chris Brunt goes over the bar.
72:56 Zoltan Gera crosses the ball, save by Scott Carson.
Correction - 70:39 James Hurst takes a shot. Blocked by Danny Murphy. Shot by Jerome Thomas from deep inside the penalty area misses to the right
of the target.
70:39 James Hurst takes a shot. Danny Murphy gets a block in. Shot by Jerome Thomas from deep inside the penalty area misses to
the right of the goal.
69:05 Chris Baird crosses the ball, clearance by Gianni Zuiverloon.
68:34 Substitution (West Brom) makes a substitution, with Simon Cox coming on for James Morrison.
65:32 Simon Davies crosses the ball, clearance made by Gonzalo Jara.
64:29 Corner taken right-footed by Simon Davies from the left by-line, assist by Simon Davies.
64:29 GOAL - Brede Hangeland:Fulham 3 - 0 West Brom Brede Hangeland finds the back of the net with a headed goal from close range. Fulham 3-0 West Brom.
63:07 Corner taken by Simon Davies.
61:45 Substitution Zoltan Gera joins the action as a substitute, replacing Diomansy Kamara.
61:45 Substitution Marc-Antoine Fortune is brought on as a substitute for Youssouf Mulumbu.
61:14 Graham Dorrans has an effort at goal from outside the penalty box missing to the wide left of the goal.
58:25 Chris Baird delivers the ball.
58:04 The ball is swung over by Damien Duff, clearance by James Hurst.
56:41 Shot by Peter Odemwingie from deep inside the penalty area misses wide to the left of the target.
55:07 Inswinging corner taken right-footed by Simon Davies, the assist for the goal came from Simon Davies.
55:07 GOAL - Clinton Dempsey:Fulham 2 - 0 West Brom Clinton Dempsey scores a headed goal from close in. Fulham 2-0 West Brom.
53:16 Damien Duff produces a right-footed shot from just outside the penalty box that misses to the left of the goal.
52:19 Peter Odemwingie challenges Brede Hangeland unfairly and gives away a free kick. Free kick taken by Aaron Hughes.
51:00 Chris Brunt concedes a free kick for a foul on Dickson Etuhu. Direct free kick taken by Aaron Hughes.
47:18 Foul by Diomansy Kamara on Chris Brunt, free kick awarded. Free kick taken by Gonzalo Jara.
46:01 Peter Odemwingie is ruled offside. Free kick taken by Aaron Hughes.
45:01 The second half kicks off.
45:00+3:26 The ref blows to signal half-time.
45:00+2:54 Inswinging corner taken from the right by-line by Damien Duff, Gianni Zuiverloon makes a clearance.
45:00+1:39 Jerome Thomas gives away a free kick for an unfair challenge on Damien Duff. Damien Duff takes the free kick.
45:00+0:26 Assist on the goal came from Dickson Etuhu.
45:00+0:26 GOAL - Simon Davies:Fulham 1 - 0 West Brom Goal scored by Simon Davies from 30 yards to the top right corner of the goal. Fulham 1-0 West Brom.
40:05 Inswinging corner taken by Simon Davies from the left by-line, Headed effort from close range by Brede Hangeland goes wide
left of the goal.
39:50 Centre by Simon Davies, save made by Scott Carson.
39:08 John Pantsil produces a cross, clearance by Gonzalo Jara.
37:09 Graham Dorrans takes a shot.
35:29 Effort on goal by Simon Davies from deep inside the penalty area misses to the right of the goal.
35:17 The ball is sent over by John Pantsil, James Hurst makes a clearance.
34:04 The ball is swung over by James Hurst.
33:33 The ball is crossed by Jerome Thomas, clearance made by Dickson Etuhu.
32:55 Substitution Nicky Shorey comes on in place of Marek Cech.
31:36 Corner taken left-footed by Damien Duff, save by Scott Carson.
27:10 Marek Cech gives away a free kick for an unfair challenge on Damien Duff. The ball is sent over by Damien Duff, Brede Hangeland
takes a shot. Save made by Scott Carson.
26:11 Clinton Dempsey has an effort at goal from outside the box which goes wide right of the target.
24:32 The offside flag is raised against Peter Odemwingie. Brede Hangeland restarts play with the free kick.
24:01 John Pantsil concedes a free kick for a foul on Jerome Thomas. Graham Dorrans takes the free kick.
23:32 Inswinging corner taken right-footed by Simon Davies, Gonzalo Jara makes a clearance.
20:54 Jerome Thomas takes a shot. Blocked by Jerome Thomas. Corner taken right-footed by Graham Dorrans, Chris Baird manages to
make a clearance. Danny Murphy concedes a free kick for a foul on Peter Odemwingie. The free kick is delivered right-footed
by Graham Dorrans from left wing, free kick awarded for an unfair challenge on James Hurst by Clinton Dempsey. Free kick taken
by Gonzalo Jara. Chris Baird sends in a cross.
18:46 Unfair challenge on Clinton Dempsey by James Hurst results in a free kick. The free kick is delivered right-footed by Danny
Murphy from left channel, Scott Carson makes a save.
17:02 Jerome Thomas takes a shot. Save made by David Stockdale.
15:30 John Pantsil produces a cross, James Hurst makes a clearance.
12:50 Damien Duff has a shot on goal from outside the area which misses right.
12:16 Peter Odemwingie takes a shot. Save by David Stockdale.
10:40 The ball is delivered by Diomansy Kamara, clearance by Gonzalo Jara.
7:27 Peter Odemwingie sends in a cross, David Stockdale makes a save.
6:51 Graham Dorrans challenges Danny Murphy unfairly and gives away a free kick. Danny Murphy restarts play with the free kick.
6:01 The ball is delivered by Damien Duff.
Correction - 4:27 Diomansy Kamara takes a shot. Save by Scott Carson.
4:27 Damien Duff takes a shot. Save made by Scott Carson.
3:43 Unfair challenge on Marek Cech by Dickson Etuhu results in a free kick. Free kick taken by Gianni Zuiverloon.
2:48 Marek Cech fouled by Danny Murphy, the ref awards a free kick. Direct free kick taken by Marek Cech.
1:51 Chris Baird produces a cross, save by Scott Carson.
0:00 The referee starts the match.
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