Match ends, Everton 2, Chelsea 0.
Chelsea manager Maurizio Sarri says his side have reached their mental "limit" after their top-four hopes were dented by Everton's second-half resurgence.
The visitors dominated possession in the first half with Eden Hazard striking the post and Pedro wasting a chance from close range.
But their profligacy was punished four minutes after the break as Richarlison headed in following a corner for his 13th goal of the season.
And the visitors' woes increased on 71 minutes when Richarlison was brought down in the area by Marcos Alonso, with Gylfi Sigurdsson scoring the rebound from his own penalty.
As a result, Chelsea failed to capitalise on their game in hand, and still sit sixth in the Premier League table, a point behind Manchester United, who they would have leapfrogged had they won. Victory would also have taken them level on points with fourth-placed Arsenal.
"We played probably the best 45 minutes of the season and then suddenly at the beginning of the second half we stopped playing; I don't know why," said Sarri.
"It is impossible that the situation is a physical problem because if it is, you can go down gradually, not in one second.
"It is very difficult for me to explain the change. Probably it is a mental block."
When asked how worried he was that Chelsea's mental situation has not been solved, Sarri said: "At the moment, this is our limit.
"If we are able to play like in the first half with consistency, then we are in another position in the table."
For Everton, a first home win since 13 January was a much-needed response following last weekend's defeat at Newcastle in which they lost 3-2 having led by two goals.
In that game, Jordan Pickford was an erratic presence in goal, but this time where there was no dip from Marco Silva's side and the England goalkeeper made a remarkable save to stop Gonzalo Higuain's deflected shot shortly after the hosts went ahead.
Everton end struggles at home
Four losses in the past six home games prior to this encounter had made Goodison Park a depressing place for Toffees fans.
Owner Farhad Moshiri has spent more than £300m since he took over the club, but an inconsistent season looked set to continue in a first half where Chelsea were well on top.
Chelsea's early dominance came despite Silva using his programme notes to ask for a "fantastic" atmosphere similar to that at the goalless draw against Liverpool two weeks ago but it was only after the break that the hosts came to life.
Andre Gomes followed his first-half shot with another rasping effort in front of the Gwladys Street End to give the home fans hope.
And Goodison erupted with delight when Richarlison headed in after Dominic Calvert-Lewin's effort was saved by Kepa Arrizabalaga.
Calvert-Lewin came close to making it 2-0 when Bernard's cross skipped over his sliding lunge but the hosts did go further ahead after 72 minutes through Sigurdsson's penalty rebound after Kepa had stopped the initial kick.
'Barkley, Barkley, what's the score?'
Chelsea will rue this chance to put pressure on their rivals bidding to finish in the top four and secure Champions league football for next season.
They still have the back-up of being able to qualify for next season's competition by winning the Europa League, and on Friday they received a favourable quarter-final draw against Slavia Prague.
But with Tottenham and Manchester United both losing last weekend, and neither of those two or Arsenal in Premier League action this weekend, it was an opportunity to make up ground.
"Of course this was important for us, so now we have less opportunities, we have to fight and defend our opportunities," said Sarri.
When asked if he was worried this form would mean they miss out on the top four, the Italian said: "If you are speaking about the second half, you are right.
"If you are speaking about the first half, we can do everything. If we play 90 minutes for eight matches like the first half, then we can do everything."
The visitors had enough chances in the first half to earn a two-goal lead as Hazard hit the post and Pedro, Higuain and Ross Barkley could not convert from close range.
When they tried to respond in the second half, they were met with stern resistance from the Everton defence who appeared to learn the lessons from their defeat at Newcastle.
Pickford made two fine saves while Yerry Mina, making his first Premier League start since 29 December, was a strong presence in defence.
Chelsea's day was summed up by former Everton midfielder Barkley, who was booed every time he touched the ball, and was substituted after 65 minutes despite an impressive first-half performance.
In the closing stages, the home fans chanted: "Barkley, Barkley, what's the score?"
That treatment all seemed fair game, but the only sour note was an object thrown towards the England midfielder after seven minutes from the Gwladys Street End which, fortunately, did not hit its target.
Man of the match - Dominic Calvert-Lewin (Everton)
'Second half was everything I want' - what they said...
Everton boss Marco Silva, speaking to BBC Sport: "I said we have to do everything different to the first half. They tried but not in the way we planned. We played forward, tried to create chances and that is our model.
"[The first half was] everything I don't want and the second half was everything the way I want to play. I could see a desire to win the game and we could challenge a team like Chelsea. I'm very proud of the players because of what they did in the second half."
Maurizio Sarri speaking to BBC Sport: "We played the first half really, really well. We could have scored in five or six different situations. We stopped playing. We didn't defend. It is incredible.
"After a first half that was so good, the level of motivation was very high and the level of application was very high then suddenly we stopped. It is very difficult to explain."
Only Fulham worse away from home than Chelsea in 2019 - stats
- Chelsea have suffered Premier League defeat at Goodison Park without scoring a goal for the first time since September 2013, when they lost 1-0 under manager Jose Mourinho.
- Everton have kept back-to-back home clean sheets in the Premier League for the first time since doing so against Fulham and Crystal Palace back in September and October earlier this season.
- Only Fulham (six) have lost more Premier League games away from home in 2019 than Chelsea (P5 W1 D0 L4).
- Despite scoring the rebound, Gylfi Sigurdsson has now missed three of his five Premier League penalties for Everton (60%). Indeed, 2018-19 is just the second Premier League season to see two different players miss at least three penalties (Paul Pogba being the other player) after 2003-04 (Alan Shearer and Ruud van Nistelrooy).
- Chelsea's Eden Hazard has now failed to score in each of his seven Premier League games at Goodison Park; his most appearances at a single away venue without finding the net in the competition.
- Richarlison has scored 12 goals in the Premier League this season; only three players have netted more in the competition in their first season at Everton (15 - Kanchelskis, Yakubu and Lukaku).
- Everton's Jordan Pickford (25 years 10 days) became the fifth youngest English goalkeeper to make 100 Premier League appearances - after Scott Carson, Joe Hart, Ian Walker and Paul Robinson.
After the international break, Everton travel to West Ham on Saturday, 30 March (17:30 GMT) while Chelsea face Cardiff City a day later (14:05 BST).
- 8André GomesBooked at 59minsSubstituted forSchneiderlinat 68'minutes
- 10G SigurdssonSubstituted forDaviesat 86'minutes
- 20BernardSubstituted forWalcottat 78'minutes
- 2RüdigerBooked at 61mins
- 30David Luiz
- 3AlonsoBooked at 36mins
- 5JorginhoSubstituted forHudson-Odoiat 74'minutes
- 8BarkleySubstituted forLoftus-Cheekat 65'minutes
- 9HiguaínSubstituted forGiroudat 66'minutes
- 10E Hazard
- Anthony Taylor
- Shots on Target
Second Half ends, Everton 2, Chelsea 0.
David Luiz (Chelsea) wins a free kick in the defensive half.
Foul by Tom Davies (Everton).
Attempt blocked. Olivier Giroud (Chelsea) header from very close range is blocked. Assisted by David Luiz with a headed pass.
Corner, Chelsea. Conceded by Idrissa Gueye.
César Azpilicueta (Chelsea) wins a free kick in the defensive half.
Foul by Dominic Calvert-Lewin (Everton).
Hand ball by Ruben Loftus-Cheek (Chelsea).
Substitution, Everton. Tom Davies replaces Gylfi Sigurdsson.
Offside, Everton. Seamus Coleman tries a through ball, but Theo Walcott is caught offside.
Corner, Chelsea. Conceded by Jordan Pickford.
Attempt saved. Callum Hudson-Odoi (Chelsea) right footed shot from outside the box is saved in the top centre of the goal. Assisted by Ruben Loftus-Cheek.
Eden Hazard (Chelsea) wins a free kick on the left wing.
Foul by Richarlison (Everton).
Attempt saved. Theo Walcott (Everton) left footed shot from the left side of the box is saved in the bottom right corner. Assisted by Gylfi Sigurdsson with a through ball.
Substitution, Everton. Theo Walcott replaces Bernard.
Eden Hazard (Chelsea) wins a free kick on the left wing.
Foul by Richarlison (Everton).
Attempt blocked. Eden Hazard (Chelsea) right footed shot from the centre of the box is blocked. Assisted by Callum Hudson-Odoi.