The Blues headed into the international break on the back of a four game winless streak, but first half goals from Dominic Calvert-Lewin and Abdoulaye Doucoure secured a timely three points.
Ancelotti’s side have been quick starters this season, and their opener came inside just 50 seconds at Craven Cottage.
Richarlison seized on a loose ball inside the Fulham and his square ball was scrambled home by Calvert-Lewin.
But despite being an absolute disaster in defence, Fulham proved they can still carry a threat on the counter, as Bobby Reid hauled them level on 13 minutes.
Michael Keane was caught out of position by Tom Cairney clever boss and Reid’s snapshot deflected past Jordan Pickford.
However, that spark of positivity was short lived for the hosts, as Calvert-Lewin netted his 10th league of goal of the season.
Alex Iwobi’s mazy run beat three Fulham defenders out wide and Calvert-Lewin arrived on cue to bury his cross.
And with their tails up, Everton stretched their lead to 3-1 just before the break as Doucoure powered home Lucas Digne’s fine cross.
Fulham continued their plan to abandon defending after the break, as Richarlison and Calvert-Lewin could and should have made it four.
But with the Toffees unable to see the game out, Fulham were handed an unexpected way back in, as Ben Godfrey fouled Ruben Loftus-Cheek inside the box.
However, Fulham’s poor luck from the spot continued as Ivan Cavaleiro slipped and ballooned his effort over the bar.
Fulham did manage to edge themselves back into as Loftus-Cheek scuffed home with 20 to go.
The hosts worked hard to force an equaliser in the closing minutes, but Everton clung on as Fulham’s misery continues.
Full Time at a goal filled Craven Cottage it’s Fulham 2 Everton 3