Pedro Neto scored twice to condemn Everton to their first defeat of the season, with Chelsea winning 2-0 at the Hill Dickinson Stadium despite losing goalkeeper Emi Martinez to a head injury.
Neto broke the deadlock within the first minute of the second half and sealed the three points during the 11 minutes of added time that followed the lengthy treatment given to the stricken Martinez.
The Argentine international was caught in a sickening head collision with Everton defender Jarrad Branthwaite and was taken to hospital.
The victory lifts Chelsea above the Toffees and into the top four of the Premier League.
After a slow start, a fiery-tempered contest came to life when Everton midfielder Harrison Armstrong lunged into a tackle on Josh Acheampong, earning the first of five first-half yellow cards.
That challenge also roused the home crowd and drove Everton on to their best spell of the game.
Thierno Barry endured another wasteful day in front of goal, the Frenchman directing a header from Jack Grealish’s cross too close to Martinez.
Chelsea have grown accustomed to fast starts under Xabi Alonso, but they had to wait until four minutes before half-time to threaten, when Moises Caicedo struck the bar from a well-worked corner.
Everton were furious that Morgan Rogers avoided a second booking just before the break following a thunderous clash with England team-mate James Garner.
That turned out to be a huge decision, as the visitors this time burst out of the blocks at the start of the second period.
Jorrel Hato reached the byline, and his low cross fell to Neto, who had time to control before firing low past Pickford.
Chelsea had not kept a Premier League clean sheet in 22 matches stretching back to January but was rarely troubled by an Everton side short on forward options despite the loss of Martinez.
The treatment for the goalkeeper threatened to stall Chelsea’s momentum as they controlled the second half.
Belgian Mike Penders came on for Martinez for his first Premier League appearance but had little to do beyond dealing with a few desperate Everton crosses.
At the other end Pickford made a fine save to deny Joao Pedro.
But Chelsea did get their second goal when Neto coolly stroked into the bottom corner after Jordan Henderson’s free-kick was blocked by the Everton wall.
