Carlo Ancelotti’s return to Stamford Bridge ended in humiliation as the Blues scored twice in each half to brush off the Toffees.
Mason Mount nearly got Chelsea off to a perfect start inside eight minutes after meeting Willian’s cross with an acrobatic effort but Jordan Pickford made an important save to keep his compatriot at bay.
Chelsea got the breakthrough moments later when Pedro played in Mount, who spun around on the edge of the area to dispatch a powerful shot low into the net.
The hosts came close to doubling their lead four minutes later when Willian fired a low shot on target after a silky Chelsea move but Pickford was equal to the task.
On the 21st minute mark, former Barcelona man Pedro beat the offside trap before putting the ball home to double his side’s lead after he was set up by Ross Barkley.
The visitors passed up the chance to get back in the game when Richarlison dispossessed Kurt Zouma to set up Dominic Calvert-Lewin, but the Englishman could not hit the target from eight-yards.
Chelsea started the second half in similar fashion as the first and quickly got their third goal six minutes after the break through a long rage effort from Willian.
Olivier Giroud poked home from Willian’s cross three minutes later to rub salts in the wounds of the Merseyside-based club.
Everton have now gone 25 games without a win at Stamford Bridge - the joint-worst away record in Premier League history with Tottenham having also gone 25 games without a win at Chelsea in the past.