Mason Mount opened the scoring on 14 minutes with a neat turn and low finish to beat Everton goalkeeper Jordan Pickford at his near post.
Chelsea's second arrived seven minutes later when Ross Barkley sent Pedro though on goal, and the Spaniard made no mistake with a crisp strike past Pickford.
Willian grabbed the third at the start of the second half with a low shot from distance before crossing for Olivier Giroud to stab home from close range.
Chelsea manager Frank Lampard handed 18-year-old midfielder Billy Gilmour his first Premier League start for the club against Everton after an impressive performance in Tuesday's FA Cup win over Liverpool.
Goal shared the two teams:
It was to prove a good decision by the Blues boss as his midfield of Gilmour, Barkley and Mount enabled the hosts to move the ball quickly and dictate the game.
The opening goal saw Gilmour roll the ball to Mount, who found Pedro out wide on the left. The Spaniard then picked out Mount in the penalty area to produce an instinctive swivel and finish to beat Pickford:
Chelsea didn't have to wait too much longer to double their advantage. Gilmour, Giroud and Barkley all combined to send Pedro clean through to score his first Premier League goal since February 2019.
Everton offered little in the way of an attacking threat. Their best chance of the first half fell to Dominic Calvert-Lewin, but the 22-year-old mis-hit his shot wide after being played in by Richarlison.
Lampard's side secured all three points with two goals in three minutes at the start of the second half to end any hope of an Everton comeback.
Former Toffees midfielder Barkley was involved again with another pass to Willian. The Brazilian was then given far too much time and space to rifle a low shot across goal and past Pickford from outside the area.
Willian then turned provider by curling in an inviting ball from the left for Giroud to poke home his second Premier League goal of the season:
Chelsea continued to create chances but could not add to their tally. Pickford palmed a fierce Pedro shot around the post, while substitute Tino Anjorin was denied by Djibril Sidibe's well-timed sliding challenge.
Meanwhile, the Blues' afternoon was marred slightly by the loss of Mount to injury:
Chelsea's comfortable lead allowed Lampard to hand some more of his youngsters game time in the second half. Academy products Anjorin and Armando Broja both came on to make their Premier League debuts on an impressive afternoon for the Blues.