Goals in each half, by Legwinski and Malbranque, sealed a win that Fulham deserved for their enterprise against a Hammers side that lacked creativity and cohesion.
After last Sunday's 3-2 success at Ipswich, Glenn Roeder reverted to his more familiar 4-4-2 formation but the spark was missing on this occasion. Hammers created precious few chances and apart from low saves to deny Don Hutchison, in the first minute, and a second half shot on the turn from sub Jermain Defoe, Cottagers' keeper Van Der Sar had little else to do.
Strikers Fredi Kanoute and Paolo Di Canio had probably their least effective games of the season, while at the other end, without the still suspended Tomas Repka, the back four often found themselves stretched by the pace and movement of Fulham's three-pronged attack.
Yet Hammers could have taken the lead in the 11th minute, when Kanoute shrugged off Finnan to run on to Hutchison's marvellous flighted pass. But from a tight angle, the Frenchman sidefooted his shot against the base of the far post.
The visitors should have equalised with the best chance of the half on 38 minutes. Hayles was given far too much space to run right through the middle and take the ball round the advancing Shaka Hislop. Christian Dailly did well to slide in and block the low goal-bound effort with his chest, before Hayden Foxe did even better with another last ditch block to deny a follow-up from Malbranque.
The Cottagers had only another five minutes to wait before they did make the breakthrough. Following a straightforward corner from the left, Hislop remained rooted to his line and Legwinski headed in unchallenged from just six yards out. With David James - who received a rousing reception on his first appearance at Upton Park since his summer move - having come through a midweek reserve game and itching to make his first team debut after injury, Hislop needed to produce a more commanding display if he is to keep the England keeper out for much longer.
To be fair, Hislop made several decent stops when called upon in the second half but he could do nothing about Fulham's second - a 15-yard strike from Malbranque after a typically rapid Fulham counter-attack. The move began with what looked suspiciously like a foul on Di Canio just outside the penalty area at the other end but Hammers' protests were waived away by referee Graham Barber.
Barber annoyed home fans and players alike with a number of decisions but, in all honesty, he was not to blame for this disappointing performance. In fact, Fulham wasted a few good chances to extend their winning margin in the second half and West Ham can have no complaints about the result.
Minute by minute:
1 - Di Canio's neat flick sets up Hutchison on the edge of the area, but the midfielder's stinging low shot is blocked by Van der Sar.
12 - Hutchison's excellent cross-field pass sets Kanoute away on the left, and the Frenchman brushes off Finnan before beating Van der Sar with a low shot that agonisingly rebounds back off the post and is cleared away to safety.
20 - Foxe and Hayles booked for ungentlemanly conduct following a scuffle on the halfway line.
26 - After a dangerous corner is cleared well by Hutchison, Collins fires an effort high over the bar.
35 - Boa Morte booked for foul on Hutchison.
36 -Winterburn's deep free-kick is flicked on by Kanoute to Sinclair, who turns and volleys high over the bar.
38 - Saha's snap-shot from the edge of the area bounces wide of the target.
39 - Hayles runs on to Collins' pass and rounds Hislop but sees his goalbound effort blocked by the chest of the grounded Dailly. Malbranque follows up three yards out but Foxe magnificently slides in to clear the danger on the goalline.
44 - GOAL. Malbranque's corner from the left is met by the head of Legwinski in the six yard box, who powers his effort past the helpless Hislop. West Ham 0 Fulham 1.
Added time: 2 minutes.
Half-time: West Ham United 0 Fulham 1.
Second half:
50 - After Winterburn is harshly adjudged to have fouled Boa Morte, Saha slices his free-kick well wide.
57 - Boa Morte's weak left-footed shot is comfortably gathered by Hislop.
60 - Good work from Kanoute and Sinclair on the right sees a deep cross drop to Courtois, whose hooked volley falls kindly for Van der Sar.
61 - Substitution for West Ham, Defoe replaces Courtois.
64 - GOAL. After Di Canio is blatantly fouled, referee Barber inexplicably waves play on and Fulham break on the counter-attack. Saha runs at the Hammers defence and slips a pass to Malbranque, who takes one touch before blasting a shot that Hislop gets a hand to but can't prevent from hitting the net. West Ham 0 Fulham 2.
70 - Defoe runs on to Di Canio's long pass and collects a Melville miscue before turning and firing a shot into the midriff of Van der Sar.
74 - Melville booked for foul on Di Canio.
74 - Substitution for Fulham, Davis replaces Saha.
76 - After Malbranque's effort is well saved by Hislop, Haylesfires his follow-up shot wide of the target.
83 - Substitution for Fulham, Goldbaek replaces Collins.
Added-time: 2 minutes.
90 - Substitution for Fulham, Stolcers replaces Malbranque.
90 - From Di Canio's corner, Dailly's header is cleared off the line and Hutchison's follow-up effort is also blocked.
Full-time: West Ham United 0 Fulham 2.