The Toffees parted company with Marco Silva on Thursday after a humiliating 5-2 defeat to Liverpool in the Merseyside Derby and put their former striker in interim charge.
Their win over Frank Lampard’s men is their fifth of the campaign and it takes them up to 14th on the table for the time being.
Everton went ahead in a trice with a goal Ferguson would have been proud of.
Good play in the middle of the park released Djibril Sidibe on the right, and the Frenchman’s cross was met with a thumping header from Richarlison, who signed a new five-year contract in midweek, into the back of the Chelsea net after five minutes.
Former Arsenal man Theo Walcott played Dominic Calvert-Lewin through in the Chelsea box ten minutes later but Kepa Arrizabalaga was on hand to thwart the Englishman’s effort.
Everton doubled their advantage five minutes after the break when Calvert-Lewin beat Kepa with a low shot after the ball broke for him in the Chelsea box.
Just two minutes later Chelsea halved the deficit through Mateo Kovacic’s speculative long range effort for his first ever Premier League goal for the Blues.
Walcott threatened an Everton third when he outwitted N’golo Kante in the 60th minute only to see his effort blocked by Kepa.
Kovacic and Andreas Christensen went close for Chelsea with long range efforts but it was the hosts who found the next goal with six minutes left on the clock.
Kepa and Zouma conspired to give the ball away in a dangerous position and Everton duly capitalized as Calvert-Lewin pounced on another loose ball in the box to poke through the goalkeeper’s legs for his second goal of the day.
