Once again too the Toffees netted in the second half and on balance they deserved to claim all the points after a gutsy and determined performance.
In the first half for the umpteenth time Everton were glad of their England keeper Jordan Pickford as he once more made several good stops to deny the visitors a lead.
Young English forward Cole Palmer was their most dangerous threat and he was a constant thorn in the host's side.
But the Blues had a few chances to on the break with Jack Harrison going close with his effort. It was however goalless at halftime after a scrappy opening forty-five minutes.
Chelsea huffed and puffed and had plenty of the ball but they were finding it very hard to break down a resolute home defence which was putting up a solid wall of resistance.
The home side weren't creating too much themselves largely looking for chance on the break, but they finally broke the deadlock through that new source of goals; Abdoulaye Doucoure.
The Mali international has become revitalised and really valuable supplier of goals under Sean Dyche and this was already his sixth of the season.
Doucoure's strike gave Everton a lead that on balance I think they deserved, although they hadn't created too many clear-cut opportunities,
Now Chelsea started to put the pressure on and the Toffees were under the cosh somewhat as they sought to preserve their slender lead.
However the backline held firm with Jarrad Branthwaite was immense again at centre-back putting in another outstanding performance. Unfortunately, he picked up another card and will miss the trip to Dyche's former club Burnley.
The Blues boss brought on Lewis Dobbin and the young forward then scored his first Premier League goal to give the home side a two-goal cushion with minutes left.
Then came the usual long added time which dragged on before finally the whistle went and Everton had three consecutive wins under their belt without conceding a goal.