Shea Lacey opened the scoring from the penalty spot with just 14 minutes played, with the 18-year-old hauled down inside the area to also win the spot-kick.
Lacey then scored again to double our lead in the capital, firing home past Cottagers goalkeeper Dino Kaiser from close range.
Fulham hit back through Farhaan Ali Wahid at the end of the first half, with his low drive getting the better of Will Murdock.
Ali Wahid then scored again just past the hour mark, cutting inside onto his left foot to dispatch his second and draw the hosts level.