Fulham, down a goal early at Goodison Park, had brought things level when Alex Kacaniklic earned a penalty and Dimitar Berbatov finished.
But Seamus Coleman cleaned up a mess in the 70th minute at the other end to restore the home lead at Goodison.
Romelu Lukaku found himself on the ball at the edge of the box with bodies around, and he played through Steven Pienaar.
The midfielder’s cross spilled through a diving Maarten Stekelenburg’s hands, and Coleman found himself with an empty net and an easy finish for the 2-1 lead.
The misery continues for Fulham, as they are still searching for their first win ever at Goodison Park in any competition, having only picked up four points in visits to the Merseyside ground in 25 league games.
For a bit it appeared they may grab something from the match, with Dimitar Berbatov having finished his second penalty in as many weeks after Alex Kacaniklic drew a foul on the edge of the box.
The visitors still have 15 minutes to search for an equalizer, live online at NBC Sports Live Extra.