Abdoulaye Doucoure opened the scoring before Lewis Dobbin's first Everton goal imposed another damaging defeat on Chelsea boss Mauricio Pochettino.
Without the penalty for breaching financial rules, which Everton are appealing, Sean Dyche's men would be four points above Chelsea in mid-table. Pochettino shuffled his pack after a dreadful display in losing 2-1 at Manchester United in midweek.
But the Argentine is struggling to solve his side's lack of a clinical edge up front, despite the club having spent £1 billion on new players in the past three transfer windows.
Chelsea were able to welcome back Conor Gallagher from suspension, while captain Reece James, Benoit Badiashile and Armando Broja came in as Pochettino made four changes.
But James' injury-hit campaign goes on as he was forced off midway through the first half. Chelsea dominated the first half but were undone by a familiar lack of punch up front.
Enzo Fernandez tested Jordan Pickford with an effort from outside the box before the England number one produced a spectacular stop to deny Cole Palmer a stunning goal from long range.
Broja was offering far more than Nicolas Jackson as a target for Chelsea to hit, but did not solve Pochettino's need for a clinical finisher. The Albanian prodded his best chance over late in the first half from Mykhailo Mudryk's teasing cross.
Everton blew Newcastle away 3-0 to move out of the relegation zone on Thursday but took time to warm to their task. It was not until after half-time that the hosts had a shot on target as Dwight McNeil's sweet strike from the edge of the box was turned behind by Robert Sanchez.
Chelsea did not heed that warning as they were cut wide open with Everton's next attack. McNeil's pass in behind was perfectly
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