Everton secured their third win in a row with a first Premier League goal for Lewis Dobbin to pile the pressure on Mauricio Pochettino
A bright first half saw Chelsea dominate possession but, as with the majorityof their season, they failed to convert chances.
Everton pressed the visitors well but headed into the break all square, with the Blues also losing captain Reece James to yet another injury.
Ten minutes into the second half and it was the home side that struck after Dominic Calvert-Lewin burst through the Chelsea back line to go one on one with Robert Sanchez.