Tony Carr's side opened the scoring in the 27th minute after dominating the opening stages of the encounter, with Freddie Eastwood striking home after some good build up play by Graeme Carrick.
The second goal came eight minutes before the break. When Fulham goalkeeper Flitney struck his goal kick straight to Leon Britton, the pint-sized midfielder took on a Fulham defender but saw his shot cleared of the line. Fortunately, the advancing Carrick made no mistake with the follow-up.
West Ham looked like going into the interval with a comfortable lead but out of the blue Fulham pulled one back, as a left wing cross by Doherty was turned into his own net by Brent Tattum.
The late goal in the first half made the second half very tense but the Hammers deservedly held on to take the three points.
Team: Jackson, Khan, Tattum, Cascione, Lumsden, Smith, Akinsete, Carrick, Allen, Eastwood, Britton. Subs Unused: Ritchie, Metitiri, Ward, Tobolewski.