A strike from Freddie Kanoute on the stroke of half time was enough to give West Ham all three points on Bank Holiday Monday.
The first half perfectly summed up Fulham's season so far with the Whites having the vast majority of possession yet failing to convert it into goals.
Barry Hayles saw Fulham's best chance of the match deflect away as he fired his shot directly at David James' legs after he was clean through in a one-on-one.
Fulham went on to rue that chance as assistant manager Christian Damiano admitted after the match.
"The big weak point for us is that we miss too many goals. We are frustrated but we know the level of each striker. Perhaps only Steve Marlet has enough experience for the Premier League.
"It's the first time Louis Saha has played at this level, he didn't play regularly in France and at Newcastle he was a substitute.
"Boa Morte has good ability in the First Division, but in the Premiership he plays better when he starts in midfield. There is less space and you need good short technique, so it is more difficult for Boa Morte to play up front.
"We're happy with Barry Hayles as he was playing in the Conference, but is now in the Premiership and has scored 11 goals."
Looking at this season's remaining games, Damiano was optimistic that Fulham will be able to get the points required for safety.
"The objective is not a big mountain, we have five games in front of us and we need to obtain five points."