The Hammers' French striker Frederic Kanoute - a transfer target for Fulham boss Jean Tigana last summer - leapt above Rufus Brevett to powerfully head home Trevor Sinclair's cross on the stroke of half-time.
Cottagers forward Barry Hayles fluffed his side's best chance of the afternoon in the eighth minute, when he was clean through but shot straight at David James.
The relegation-threatened hosts wasted bucketfuls of possession throughout this disappointing match, with their pattern of play adhering to their season-long tendency of pretty passess in midfield - but absolutely no punch upfront.
Glenn Roeder's men, happy to soak up the pressure and aim for Kanoute with long balls out of defence, condemned FA Cup semi-finalists Fulham to their seventh defeat in their last eight league games.
Tigana had revamped his strikeforce for the capital derby. French international Steve Marlet, scorer of the goal that earned the Londoners a point in Saturday's 1-1 draw at Southampton, was dumped on the bench.
Hayles' forward partner was the out-of-form Louis Saha, who has endured a miserable season in front of goal and managed just seven league goals.
Roeder kept faith with Kanoute, who was booed after missing chances in Saturday's 3-1 success against Ipswich.
Before kick-off, the 20,000 supporters packed into Fulham's tight ground stood for an immaculately-observed minute's silence in memory of the Queen Mother.
The National Anthem was also played, after which West Ham captain Paolo di Canio turned to applaud the crowd for their tribute.
Hayles missed his great opportunity to put his side in front in the eighth minute, after Saha's precise pass into the box.
David James raced from his goal and Hayles thumped the ball against his legs - with Sylvain Legwinski slicing the rebound over the crossbar.
West Ham left-back Vladimir Labant was substituted with a back injury at the half-way point in the first period, after crashing to earth following an aerial challenge with Saha. He was replaced by Ian Pearce.
The game moved up a notch around the half-hour mark.
First, the visitors' first half-chance arrived when di Canio's through-ball was just beyond Sinclair's reach.
And play swung almost immediately to the other end for Fulham to go close to scoring - but Steed Malbranque could not quite reach Saha's cross.
West Ham's first real opening, on the stroke of half-time, gave them a 1-0 lead.
Sinclair played a neat one-two with Steve Lomas on the left wing and chipped to the far post - where Kanoute towered above Brevett and headed firmly into the bottom corner of Edwin van der Sar's goal.
Tigana must have been frustrated by his side's strange reluctance to shoot in the first half. Malbranque, the energetic France Under-21 international, changed in the 49th minute - with a curling 25-yard free-kick that flew a foot over James' bar.
But Fulham were still enjoying the lion's share of possession and territory and Christian Dailly made a crucial interception as Legwinski prepared to head a John Collins cross towards goal.
Roeder made a controversial substitution in the 66th minute. He hauled off the ineffective di Canio and replaced him with John Moncur.
The sullen-faced Italian was clearly unimpressed with his manager's decision and marched off the pitch, grabbed his jacket and stomped straight past the bench and down the tunnel.
Fulham sub Jon Harley was agonisingly close to scoring with his first touch.
He met Steve Finnan's bouncing cross with an awkward header but the ball brushed the outside of James' left-hand post as it drifted wide.
Finnan lashed a spectacular 20-yard volley over the top late on and Fulham keeper van der Sar even tried his luck with a header from an injury-time corner, but the ball flew wide.