Louis Saha and Jack Rodwell both scored in the closing stages to hand Everton a dramatic 3-1 at Craven Cottage.
The Toffees were up inside two minutes thanks to a wonderfully taken goal by on loan Real Madrid midfielder Royston Drenthe.
However, Fulham levelled through £10.6 million summer signing Bryan Ruiz, before Saha and Rodwell snatched three points after Bobby Zamora missed an open goal.
Firstly Saha stroked past Mark Schwarzer almost immediately after Zamora's howler and Rodwell made sure of the result with an expert drive from the edge of the area.
Everton are now up to 13th in the Barclays Premier League following their first win in four games.
Fulham, meanwhile, sit one place above the relegation zone having mustered only seven points in their opening nine fixtures.