Attacker Clint Dempsey went the full 90 but defender Carlos Bocanegra was subbed in the 14th minute after clashing heads with West Ham's Freddie Ljungberg as Fulham went down, 2-1.
Defender Jonathan Spector went the distance for West Ham.
Fulham is in second-to-last place, five points deep in the relegation zone. It was won only twice in 22 games this season.
Goalkeeper Tim Howard had a quiet day as Everton beat Manchester City, 1-0, to remain in fifth place while continuing its quest to challenge the English Premier League's big four - Liverpool, Chelsea, Arsenal and Manchester United.
Everton is tied on points with fourth-place Liverpool, which has a game in hand. But it is eight points behind Chelsea and 12 behind Arsenal and Manchester United.
The EPL's top four teams qualify for the Champions League while the fifth place finisher earns a UEFA Cup berth.
Reading, with goalkeeper Marcus Hahnemann (90 minutes) and midfielder Bobby Convey (17 minutes) fell 3-1 to Aston Villa. Reading is in 13th place but only two points above the relegation zone.