Chelsea dominated throughout and deserved their two-goal interval lead, both from headers.
Ashley Cole’s floated cross was headed home by Daniel Sturridge on the half-hour mark, and the lead was doubled in first half-injury time as Blues skipper John Terry bundled home a Frank Lampard free kick on his 350th appearance for the Londoners.
The game was wrapped up on the hour mark as Juan Mata set up the chance for Ramires to finish from close range.
Everton rallied for a goal with nine minutes remaining as substitute Apostolos Vellios replied with his first touch of the ball.
The only disappointment for Chelsea boss Andre Villas-Boas will be the Blues negligence at the back, as they have now gone seven games without keeping a clean sheet, their worst run since September 2003.
Referee: Mike Jones
Venue: Stamford Bridge
Chelsea scorers: Sturridge 31, Terry 45, Ramires 62
Everton scorers: Vellios 81
Yellow cards: Fellaini (EVE), Baines (EVE), Cole (CHE), Sturridge (CHE)