The only goal of the game at Goodison Park came from a penalty in the ninth minute of added time in the first half.
Jorginho stepped forward and safely put in 1-0 for the guests from London.
The additional minutes were added after an incident that occurred already in the tenth minute.
Everton’s defender Ben Godfrey saved his own mistake but in connection with it received a blow in the duel with Chelsea’s Kai Havertz.
Godfrey immediately grabbed his right leg and waved for assistance before minutes later he was forced off the pitch on a stretcher.
“We can confirm that Ben Godfrey has suffered a lower leg injury and has been taken to hospital. We are all with you,” Everton wrote on Twitter at half-time.
Also in the second half, a longer extra time was added, ten minutes in total.
But that desperate pursuit of an equalizer from Everton didn’t really show, possibly because Chelsea played the match smartly.
It was 1-0 to Chelsea in all who face Tottenham in the next round. For Everton, it is important to take new measures against Aston Villa away next weekend.