After going close on several occasions in a goalless first half, Hammers took the lead on 60 minutes when Collington cut inside from the right and curled a superb left-foot shot past the Fulham goalkeeper.
However, rather than lead to a comfortable victory for Hammers, the goal seemed to spur the visitors into life, and they equalised on a breakaway attack with 20 minutes remaining.
A draw appeared likely as the clock ran down with neither side showing any real signs of attacking quality, but Fulham snatched the win two minutes into injury time when a second successive corner was bundled home.
Said Tony Carr: "It was very disappointing to lose the game in that manner, especially as I didn't think we deserved to come away with nothing. A draw would probably have been a fair result but, saying that, we had plenty of chances to win the game.
"Greg Pearson and Marce Collington both missed very good opportunities in the first half, when we had long spells of superiority, and once we got the goal I thought we would go on to win comfortably.
"They fought back well, though, and got the breaks when it mattered. I am disappointed, but there were some good signs, and it was a big improvement on last week's performance at Sheffield United. If we can start taking our chances, I am sure the first win will come soon."
Team: Behcet, McClenahan, Tattum, Laws (Blewitt 80), Lumsden, Tucker, Wright, Bunce, Cohen, Pearson (Lee 75), Collington (Carrick 75). Sub unused: Parrington.
by Danny Francis