Fulham captain Brian McBride, making his first start since recovering from a knee injury, provided a subdued performance. Defender Carlos Bocanegra and keeper Kasey Keller spent the game on Fulham's bench.
McBride volleyed straight at keeper Robert Green and his shot on a rebound was blocked by defender Lucas Neil. Dempsey also shot straight to the keeper on one chance and too weakly on another.
Johnson, who joined Fulham from the Kansas City Wizards on a $3.2 million transfer in January, shot far wide on his one chance.
American defender Jonathan Spector was a 90th minute sub for West Ham, which won on an 87th minute goal by Peruvian Nolberto Solano.
Reading, with Marcus Hahnemann in goal, fell, 2-1, to Aston Villa to give the Royals a club record eight-straight league defeats. (Bobby Convey did not suit up for Reading.)
Neither Eddie Lewis nor Benny Feilhaber saw action in Derby's 2-0 loss at Wigan.
ENGLISH PREMIER LEAGUE RELEGATION BATTLE
Place Team Goal-Dif. Pts
15. Sunderland -20 26
16. Bolton -12 25
17. Birmingham -13 23
---------- Relegation Zone -----------
18. Reading -24 22
19. Fulham -20 19
20. Derby -44 9