The Toffees put an end to Chelsea’s 17-game unbeaten run in all competitions as Frank Lampard’s side tasted defeat in the Premier League for just the second time this season.
Gylfi Sigurdsson scored the only goal of the match from the penalty spot in the first half after Edouard Mendy brought down Dominic Calvert-Lewin in the box.
Everton made life for their opponents difficult with a determined defensive display at Stamford Bridge.
Although Mason Mount hit the woodwork twice in the second period, the Blues were not at their best going forward.
The result meant the west Londoners were unable to close the gap on league leaders Tottenham.
And Mount admitted that if his side harbour ambitions of challenging for the title, they must not begin games so sluggishly.
‘We know we didn’t start well enough, we didn’t start like we have been playing recently and then we got punished. From 1-0 down it is a difficult game, so we have to look at how we started and correct that for the next game.
‘These things happen sometimes but we want to be pushing for number one and we can’t start like that. We know that.
‘We are always going to create but in this game we didn’t put them away but that is sometimes how it goes and we have to look towards the next game.’