Everton eased the pressure on Marco Silva and dented Chelsea's top-four hopes with a morale-boosting 2-0 win at Goodison Park on Sunday.
Richarlison punished Chelsea's profligacy just after half-time and Gylfi Sigurdsson converted the rebound from his own saved penalty to secure only the Toffees' second victory in nine Premier League games at home.
Marco Silva's men, who dramatically lost 3-2 at Newcastle United last time out, were thoroughly outplayed in the first half, but an improved performance from Jordan Pickford helped keep the visitor at bay.
Defeat for Chelsea, its first since the EFL Cup final, leaves it three points adrift of fourth-placed Arsenal with eight games remaining.
Panic permeated Everton's defence in the opening exchanges as it opponent twice went close in quick succession.
Eden Hazard first drove a deflected shot into the base of the upright, before Gonzalo Higuain's scuffed finish from Jorginho's inventive pass allowed Michael Keane to hack the ball clear.
Pickford had earlier denied Hazard at his near post and, after Pedro dragged marginally wide, will have welcomed half-time.
However, Everton emerged from the interval transformed and Richarlison nodded it ahead in the 49th minute when Kepa Arrizabalaga parried Dominic Calvert-Lewin's header straight to the Brazil forward.
Marcos Alonso hit the side-netting with a good chance to respond and compounded that miss by tripping Richarlison in the box at the other end.
Sigurdsson stepped up 18 minutes from time and, after seeing Kepa save his initial attempt, pounced on the rebound to complete Everton's first win in this fixture in seven attempts.
What does it mean? Europa League could be Chelsea's last chance saloon
Chelsea really only had itself to blame for allowing Everton to seize control of this contest and will now find it difficult to overhaul both Arsenal and Manchester United in the run-in.
With that in mind, Maurizio Sarri might be well advised to focus more energy on the Europa League - in which it is through to the quarterfinals - as a best route into next season's Champions League.
Pickford stands up under pressure
Toffees boss Silva asked for Pickford to show "more emotional balance" after his erratic display at St James' Park and the keeper answered the call on Merseyside.
His early denial of Hazard set the standard for an assured performance that featured five saves in total, most of which arrived when under considerable pressure in the first half.
Sarri errs with Alonso selection
He impressed in the 5-0 thumping of Dynamo Kyiv in midweek but left-back Alonso, chosen ahead of Emerson Palmieri, was again found out when required to perform more defensive duties.
It was the 28-year-old's error that sent Sigurdsson to the spot in the second half and he should also have done better with an earlier chance to draw Chelsea level.
Everton's first assignment after the international break is a trip to fellow mid-table team West Ham on March 30. Chelsea visits relegation-threatened Cardiff City the following day.
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