Chelsea's hopes of a top-four finish were dented as Everton finally ended a 25-match run without a win against a top-six side with a 2-0 victory.
The Toffees' record against the Premier League's established powerbase is poor with their last success over one of them being a 4-0 hammering of Manchester City in January 2017.
On the evidence of their opening 45 minutes, it never looked likely they would end that sequence but capitalised after the visitors failed to take advantage of their early dominance.
The one constant Everton have shown this season is just how inconsistent they are and that flaw was encapsulated within the space of 90 minutes.
Woeful and timid in a first half in which the visitors should have pressed home their advantage, they returned after the break a different side with goals from their joint Premier League top scorers Richarlison and Gylfi Sigurdsson, who now both have 12.
By contrast, Chelsea's two best performers Eden Hazard and Ross Barkley - one of seven changes from Thursday's Europa League victory over Dynamo Kiev - faded in the second half.
Barkley was making his first appearance at Goodison Park since May 2017 and his every touch was booed following his acrimonious departure the following January having not played a match in the season because of injury.
He and Hazard dictated most of the first-half play which saw the Belgium international twice threaten: Jordan Pickford saving one effort and watching a second rebound off a post.
Everton played like a team who had one home league win since November, concentrating on containment rather then creativity and lacking in intensity, and it allowed the visitors to control the game.
Jorginho, Gonzalo Higuain and Pedro all had half-chances but, incredibly, the best opportunity fell to Dominic Calvert-Lewin who should have scored with an unmarked header eight yards out just before the break.
Everton came out after the interval a different side and the positivity which was so lacking in the first half paid off within four minutes.
Calvert-Lewin's downward header at a corner was parried by Kepa Arrizabalaga but Richarlison reacted quickest to nod home the rebound - Everton's first league goal against Chelsea since January 2016.
Pickford, criticised for his role in the defeat at Newcastle last week, threw himself to his left to brilliantly save Higuain's deflected half-volley.
Chelsea boss Maurizio Sarri made a double change with Ruben Loftus-Cheek and Olivier Giroud replacing Barkley, much to Goodison's delight, and Higuain.
However, it did little to change the momentum with Hazard now a peripheral figure and - 18 minutes from time - the hosts delivered the killer blow when Marcos Alonso brought down Richarlison and Sigurdsson scored with a rebounded penalty after Kepa saved his initial effort.
Chelsea remain three points behind fourth-placed Arsenal and still have to go to Liverpool and Manchester United.
With the teams above them in better form, winning the Europa League - with Chelsea in the quarter-finals and on the easier side of the draw - may now be their best chance of securing Champions League football this season.