Roberto Martinez made two changes to the side that earned a 1-1 draw with Arsenal, with Gerard Deulofeu replacing Kevin Mirallas and Leon Osman replacing the suspended James McCarthy.
And it was Leon Osman who gave Everton the lead on 18 minutes. After some great work down the left, Osman received a pass from Steven Pienaar and stroked a fantastic left footed finish beyond Stekelenberg. 1-0 Everton
Everton proceeded to dominate the first half with Deulofeu, Lukaku, Osman and Coleman all coming close to doubling EvertonÂ´s lead as the Blues chased a second goal.
Fulham came out stronger after the break and sustained a good spell of possession and should have equalised through Scott Parker but Tim Howard saved well.
Howard then stopped Steve SidwellÂ´s effort and then saw Alex Kacaniklic fire over and into the Gwladys Street from six yards out.
Deulofeu was stretchered off on 64 minutes with what looked to be a hamstring injury, replaced by Kevin Mirallas
On 67 minutes Fulham got the equaliser their second half performance arguably deserved. Gareth Barry was alleged to have fouled Kacaniklic to concede a penalty which Berbatov casually converted. 1-1.
Everton responded emphatically.
Attacking down the left, the impressive Steven Pienaar attempted to square the ball to Kevin Mirallas but goalkeeper Stekelenberg got his hand to it, only for the ball to fall to Seamus Coleman to tap into an empty net. 2-1 Everton.
Everton then made it 3-1. A corner was delivered from the right, finding the head of Distin, to deflect off Lukaku, hit Stekelenberg foot, to then deflect off Lukaku again to bounce up kindly for Gareth Barry to head home from a yard out.
Kevin Mirallas made it 4-1 on in injury time with a long distance effort to seal what turned out to be a comfortable win.