Chelsea’s bad luck continued as they lost points on a disappointing night for them at Stamford Bridge.
Mason Mount scored for the Premier League’s fourth straight game to give them the lead with 20 minutes left.
But injured Everton fought back with Jarrad Branthwaite’s equalizer four minutes later.
The result leaves third-placed Chelsea four points behind leaders Manchester City.
They were without a recognized attacker, Romelu Lukaku, Timo Werner and Kai Havertz all being absent.
Lukaku, Werner and Callum Hudson-Odoi were unavailable after testing positive for Covid-19 with Ben Chilwell, who came out with a knee injury anyway.
Havertz is ill and is awaiting follow-up test results after initially testing negative for Covid.
Christian Pulisic led the attack, supported by Hakim Ziyech and Mount.
Ziyech was the star player in a Chelsea-dominated first half without scoring.
They had 81% possession and 13 shots on goal in those opening 45 minutes, but failed to pass Everton goalkeeper Jordan Pickford, who made saves to prevent Reece James, Mount and Pulisic .
And Ruben Loftus-Cheek missed a great opportunity for Thomas Tuchel’s side at the start of the second half when he headed from close range.
Everton then took advantage of a threat spell on the counterattack – but got hit at the break for the opening goal.
After Thiago Silva brilliantly dispossesses Abdoulaye Doucouré, Chelsea leap forward and James pass the ball to Mount, who shoots home.
But the hosts then went extinct on the other end. Anthony Gordon took a free kick from the left and Branthwaite scored at the far post.
Chelsea: Mendy, Azpilicueta (Chalobah 78), Silva, Rudiger, James, Loftus-Cheek (Barkley 65), Jorginho, Alonso (Saul 65), Ziyech, Mount, Pulisic.
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