Pedro Neto's double condemned Everton to a first defeat of the season as Chelsea won 2-0 at the Hill Dickinson Stadium despite the loss of goalkeeper Emi Martinez to a head injury.
Neto opened the scoring inside the first minute of the second half and secured the three points during the 11 added minutes following the lengthy treatment given to the stricken Martinez.
The Argentine international was involved in a sickening head clash with Everton defender Jarrad Branthwaite and was taken to hospital.
Victory lifts Chelsea above the Toffees into the top four of the Premier League.
After a slow start, a fiery-tempered encounter sparked into life when Everton midfielder Harrison Armstrong launched into a tackle on Josh Acheampong for the first of five first-half yellow cards.
That challenge also enlivened the home crowd and spurred Everton on to their best spell of the game.
Thierno Barry was guilty of another wasteful day in front of goal as the Frenchman planted a header from Jack Grealish's cross too close to Martinez.
Chelsea have made a habit of fast starts under Xabi Alonso, but it took until four minutes before half-time to threaten when Moises Caicedo blasted off the bar from a well-worked corner.
Everton were furious that Morgan Rogers escaped a second booking just before the break after a thunderous clash with England team-mate James Garner.
That proved to be a huge decision as the visitors this time flew out of the blocks at the start of the second period.
Jorrel Hato got to 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 were rarely troubled by an Everton side short on forward options despite the loss of Martinez.
The treatment for the goalkeeper threatened to halt Chelsea's momentum as they controlled the second half.
Belgian Mike Penders replaced Martinez for his first Premier League appearance but had little to do bar 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
Latest stories
US News US goes on the offensive in Central Asia
It's dealmaking time: despite the roiling geopolitical tensions embroiling Washington on several fronts, US Secretary of State Marco Rubio arrived in Central Asia's Uzbekistan Sunday to boost commercial ties -- and...
Europe 'Like we had a war': France counts cost of violent protests
France was reeling on Sunday from widespread damage caused by violent protests the day before that saw 1,800 people arrested, a historic town...
Europe Kremlin says Ukrainian attacks won't change war aims as Kyiv hits Saint Petersburg
The Kremlin on Sunday said Ukrainian large-scale attacks on Russian cities will not change its war aims as Kyiv hit Saint Petersburg with the biggest drone attack on Vladimir Putin's hometown since...