Chelsea will never find their way into the top four at this rate. They dominated for much of the game without being able to come up with an end product, eventually conceding from the almost inevitable set piece to send Everton on the way to their first home win since mid-January.

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It just is not happening for Maurizio Sarri and his players at the moment, not in front of goal at any rate. Eden Hazard is becoming anonymous, something difficult to envisage at the start of the season, Gonzalo Higuaín is not intimidating defences and an inventive and industrious midfield is still failing to provide backup in the form of a goal threat. Chelsea could have been out of sight by the interval yet Everton were practically invited to come back into the game, which they did through second-half goals from Richarlison and Gylfi Sigurdsson.

“We showed great attitude and character in the second half, but we could have been behind at half-time but for Jordan Pickford,” Marco Silva said. “He was fantastic, he kept us in the game.” Sarri did not disagree. “We could have scored four or five goals in the first half but in the second half we stopped defending,” the Chelsea manager said.

Facebook Twitter Pinterest Richarlison reacts the fastest to pounce on a rebound and give Everton the lead. Photograph: James Speakman/Mercury Press/Rex/Shutterstock

Pickford has had his ups and down in recent weeks but the Everton goalkeeper came to his side’s rescue as early as the sixth minute, getting down low at his near post to keep out a shot from Hazard after Marcos Alonso had played the forward into the area. That was already an ominous sign for the home side, and when Hazard hit the post a minute later, quickly followed by Michael Keane having to clear up on the line from Higuaín, the Goodison crowd began to express disapproval. By that stage in the game Everton had barely been out of their own half.

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Ross Barkley’s every touch was booed on his first return to his former club, and when the England player deftly outsmarted Everton’s cover in the area to open up the possibility of a shot from a narrow angle he rather spoiled the effect by blasting the ball wastefully across the face of goal. Barkley managed a little better a few minutes later, bringing a routine save from Pickford from the edge of the area, as did Jorginho when he arrived at speed to take a short pass from Higuaín, only to shoot straight at the goalkeeper.

Everton had advanced over the halfway line a couple of times by the mid-point of the first half – though apart from Dominic Calvert-Lewin shooting too high, only a low drive by André Gomes managed to bring Kepa Arrizabalaga into action. Chelsea looked the side most likely to break the deadlock, and Pedro should have managed it on the half hour from Alonso’s return pass, instead of missing the target by a distance with a clear sight of goal.

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With Hazard operating mostly wide on the left to only limited effect, Pedro looked the player most likely to create something from nothing, even if his finishing left something to be desired. Towards the end of the first half he picked his way deftly through a clutch of defenders to give himself room for a shot from the edge of the area, only to see his effort fly harmlessly. Despite being outplayed for most of the first half the home side would still have been annoyed with themselves at the interval, for when a chance arrived to score from a set piece – realistically Everton’s best hope of going ahead – they squandered it. There was nothing wrong with Sigurdsson’s well-flighted free-kick, and nothing to fault in the way Calvert-Lewin reached the ball ahead of the Chelsea defence, but having earned himself a free header from eight yards out he put it too high.

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Although Everton started the second half with a declaration of intent when a rasping shot from Gomes brought a decent save from Arrizabalaga, when the home side made a mockery of what had gone before by taking the lead within four minutes of the restart it was in fact from a set piece and it again involved Sigurdsson and Calvert-Lewin. The latter climbed highest to meet the former’s corner, and though his downward header was saved on the line the ball sat up invitingly for Richarlison to tuck away for his first Everton goal against top six opponents. Everton would have been happy with that, but just after Sarri had made his second-half substitutions – Barkley’s number going up was greeted by a roar of delight – Alonso stepped on Richarlison’s foot in the area and Sigurdsson accepted the opportunity to make it two.

Though Arrizabalaga saved the initial penalty, he only pushed the ball back to let Sigurdsson score at the second attempt. Just about the only bright spot for Chelsea in the whole of the second half was a rising drive by Callum Hudson-Odoi that Pickford needed to tip over. Probably not enough to enliven the long journey home.