Hammers scrambled a point thanks to Trevor Sinclair's 64th minute penalty after Facundo Sava gave the Cottagers the lead four minutes into the second half.
To add insult to injury, Tomas Repka was sent off for the third time in his Hammers career and was barracked by the West Ham fans as he disappeared down the tunnel in injury time of this poor London derby.
The Czech Republic international defender's disgraceful disciplinary record now reads 25 yellow cards in 53 appearances. Referee Dermot Gallagher doesn't dish out cards lightly but even he chose to caution the reckless Repka for dissent twice in a minute.
''I understand the supporters being angry and disappointed with Tomas and I'm not going to make excuses for him. He knows he's done wrong,'' admitted an honest Glenn Roeder afterwards.
It meant Ian Pearce, introduced as a 66th minute substitute for returning striker Fredi Kanoute, had to fill in alongside Christian Dailly in central defence as Hammers focused on keeping a point rather than pursue the three they so badly needed.
But neither side showed enough quality to warrant a win. Hammers, still looking for their first home win this season in 12 attempts, were very fortunate not to concede a bizarre gift of a goal after just seven minutes. Goalkeeper David James drove the ball against Sava but, luckily, it rebounded wide of the empty net.
There was another let off seven minutes later when Repka misread the pace on the ball and Steve Marlet nipped in between him and the onrushing James, who seemed to impede the French forward on the edge of the penalty box.
James would regain his composure to pull off a point-rescuing save but Marlet remained a constant threat to the home back four. West Ham did create the best chances of the first half, though.
Kanoute, starting his first match since tearing his groin muscle at Chelsea on September 28, made little impact but he lit up a drab, disjointed first half with a skilful turn before finding Schemmel wide on the right. Steve Lomas met the Frenchman's cross on the volley, six yards out, but fired over the bar.
Michael Carrick, once again the best in a claret and blue shirt, should have given his side the lead but could only prod the ball at keeper Maik Taylor following Jermain Defoe's shot on the turn.
Defoe then went close himself when he rapped the outside of the post direct from a free-kick on the stroke of half-time.
Those misses proved costly, for Fulham opened up West Ham in the 49th minute on the right flank, where a low cross found Sava, who had the easiest of tap-ins at the far post. Once again, questions were being asked of a defence caught ball-watching and leaving players unmarked.
Going forward, Hammers caused Alain Goma and Andy Melville few anxious moments. Understandably, Kanoute will need time to regain his touch and match fitness but the lack of movement between him and Defoe meant West Ham's midfield always struggled to find an outlet.
Joe Cole was too often isolated out wide on the left, while Sinclair made little impression against Rufus Brevett on the opposite flank. Carrick and Lomas huffed and puffed but created little until the England midfielder's right-wing corner led to the equaliser.
Dailly's second header struck the arm of Sylvain Legwinski and upped stepped Sinclair to score his first penalty in the Premiership.
With Kanoute a fading force, Glenn Roeder brought on Pearce to resume his makeshift striking role but it was Fulham who wasted the best chances to go in front.
Twice in a minute Marlet should have scored from great positions, but credit James for keeping out his first effort with a fingertip save against the post. In a Jekyll and Hyde performance by the West Ham and England keeper, this was one moment for him to savour.
Don Hutchison also came off the bench (for Lomas with 13 minutes remaining) and did well enough on the right of midfield, which enabled Cole to move inside and Sinclair to switch to the left. Hutch managed to get his head to a Cole cross and his contribution, especially in terms of goals, could be crucial in the coming months.
But hopes of snatching a late winner were dashed when Repka let himself and Hammers down with four minutes to go. ''Inexcusable,'' said Roeder, clearly unimpressed with the foolishness of his experienced Czech defender.
Rather than gamble on trying to win the game at that late stage, Roeder moved Pearce back and left Defoe alone up front for the final few minutes.
The manager is the first to admit that Hammers have now taken just two points from two home games - against Bollton Wanderers and Fulham - where all six were needed.
Roeder said: ''Some of our away performances have been much better and that's what we're going to need at Blackburn and Charlton.''
Minute-by-minute:
7 - David James almost gifts Fulham an amazing opener, as he inexplicably whacks a simple clearance straight at the onrushing Sava on the edge of the penalty area. However, the Hammers goalkeeper's blushes are spared, as the ball bounces just wide of the target.
12 - Kanoute proves just why he has been missed so much, as a stunning piece of control and clever turn on the halfway line allows him to sweep a pass out to Schemmel, whose low cross is volleyed just over by Lomas - who is adjudged offside anyway.
14 - Hammers are let off the hook again, as a long ball over the top isn't dealt with by Repka, who tries to shepherd the ball back to James with Marlet breathing down his neck. The Hammers keeper isn't out quick enough, though, and Marlet nips in to clip the ball on, and thankfully wide for a goal kick.
17 - Carrick's corner from the right is met by Dailly, whose powerful header is goalbound until Brevett chests it round the post for another corner.
24 - Hammers go close again, as Sinclair lays a ball back to the edge of the area for Lomas, whose shot cannons of referee Gallagher and falls nicely for Defoe. The youngster's effort is only parried by Fulham keeper Taylor, and Carrick can't convert the follow-up.
36 - Finnan's deep cross from the right is met by Legwinski, whose right-foot volley from 12 yards out is comfortably held by James.
41 - Kanoute's dangerous low cross from the right reaches Sinclair, whose near post half-volley is well held by Taylor.
Added time: 1 minute
45 - After Goma's handball some 25 yards out, Defoe's direct free-kick crashes against the post and rebounds back into play as the referee blows the whistle for half-time.
Half-time: West Ham United 0 Fulham 0.
Second Half:
49 - GOAL. Hammers are caught napping at the start of the second half, as Marlet combines on the right with Finnan, who skips past Cole into the penalty area and fires a low cross into the six yard box that beats Dailly and Schemmel and is stabbed home by an unmarked Sava at the far post. West Ham United 0 Fulham 1.
57 - Winterburn's deep cross from the left is headed on by Lomas to Sinclair at the far post but, rather than attempt to bring it down, the midfielder attempts a spectacular scissors kick that flies high over the bar.
61 - Cole's perserverance sees him push the ball out wide to Lomas, whose deep cross reaches Winterburn, but the defender heads the ball over.
64 - Carrick's deep corner is headed down by Dailly, who gets another chance as the ball bounces up, and his second effort clearly strikes the arm of Legwinski. Referee Gallagher has no hesitation in awarding a penalty.
65 - GOAL! Trevor Sinclair steps up and fires the spot-kick confidently into the left-hand bottom corner to the relief of the Upton Park crowd. West Ham United 1 Fulham 1.
65 - Substitution for Fulham, Djetou replaces Legwinski.
67 - Winterburn booked for foul on Malbranque.
68 - Substitution for West Ham, Pearce replaces Kanoute.
68 - Sava's flick-on reaches Marlet, who prods the ball towards the far corner with James seemingly beaten. However, the Hammers keeper somehow launches himself across to palm the ball against the post and then bravely block the rebound to clear any further danger.
69 - Marlet gets a yard of space again, this time on the edge of the area, but fires his effort just past the post.
75 - Carrick's corner is met by Repka, who volleys high over the bar from 12 yards out.
77 - Substitution for West Ham, Hutchison replaces Lomas.
78 - Substitution for Fulham, Goldbaek replaces Malbranque.
85 - Cole's cross from the left is headed goalwards by Hutchison at the far post, but Taylor stretches superbly to tip the ball round for a corner.
89 - Substitution for Fulham, Hammond replaces Sava.
90 - Wome's deflected cross drops nicely into the path of Marlet, who turns and fires his shot over the bar.
Added time: 4 minutes.
90 - Repka booked for dissent.
90 - After continuing to argue with the referee, Repka is booked again for dissent and shown a red card.