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 Martínez 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 Martínez.
The Argentine international was involved in a sickening head clash with Everton defender Jarrad Branthwaite and was taken to hospital.
"As far as I know he left the stadium conscious. Right now he's in hospital doing precautionary tests, so let's see," said Chelsea boss Xabi Alonso.
A first away win of the season lifts Chelsea above the Toffees into the top four, while the Blues also recorded a first clean sheet in 23 Premier League games.
"We needed one of these wins away. We played very professionally, very seriously, looking solid. It is a very good win," added Alonso.
"We need to get many more clean sheets for the rest of the league games, but for sure the first one of the season feels good and now we need to keep going this way."
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.
'More Flair'
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 Martínez.
Chelsea have made a habit of fast starts under Alonso, but it took until four minutes before half-time to threaten when Moisés 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 Jordan Pickford.
Chelsea had not kept a Premier League clean sheet since January, but were rarely troubled by an Everton side short on forward options despite the loss of Martínez.
"I just felt that Chelsea had that little bit more flair and ability which we didn't possess at the right moments today," said Everton boss David Moyes.
The treatment for Martínez threatened to halt Chelsea's momentum as they controlled the second half.
Belgian Mike Penders replaced the Chelsea number one 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 João 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.
AFP