For more than an hour it remained goalless at Goodison Park but the air of confidence Antonio Conte's side carry meant it never felt as though they were in danger and there was a certain inevitability about the goals from Pedro, Gary Cahill and substitute Willian in the final 25 minutes.
That was not taking anything away from their opener - an unstoppable strike from the former Barcelona forward - but it was another of those typically attritional performances in which their quality ultimately shines through.
The Premier League leaders began the day four points ahead of Tottenham, kicking off later in the north London derby at home to Arsenal, knowing any slip would give their rivals all the ammunition they needed to ramp up the pressure in the title race.
That opportunity never materialised as Chelsea became only the second team to win a league match at Goodison in the last year, with the Toffees having gone eight matches unbeaten at home since December.
Everton were missing Morgan Schneiderlin, who sustained a thigh injury in training on Friday, and with Idrissa Gana Gueye tasked with the man-marking job on his former Lille team-mate Eden Hazard it effectively left the hosts one short in midfield.
Thankfully they had energetic 18-year-old Tom Davies prepared to put in the leg work with fellow youngster Dominic Calvert-Lewin dropping back to assist on the left.
However, Calvert-Lewin could have had an even greater impact going the other way as inside 70 seconds his near-post shot beat Thibaut Courtois but rebounded off the upright and Lukaku's shot was blocked by Cahill.
Gueye's job for the day meant there were going to be some teething trouble in the areas he usually patrolled and that allowed Cahill to advance and fire in a shot which Maarten Stekelenburg fumbled and Ashley Williams was on hand to hack clear.
The defender's decision to try to nick the ball of Diego Costa on halfway backfired when the striker turned to run into the space behind and then release the Gueye-free Hazard who rounded the goalkeeper but fired into the side-netting.
Hazard escaped Gueye's attentions again when he ran from deep and advanced 40 yards down the middle of the pitch only for the attack to falter when Davies charged back to dispossess Costa, who was guilty of Chelsea's worst miss when he volleyed over from eight yards having got the wrong side of Phil Jagielka.
The debate over Romelu Lukaku's future continues to rumble on with the striker refusing to sign a new contract and Chelsea reportedly ready to re-sign him in the summer but if this was the close-up audition it was not convincing.
Admittedly the Belgium international did not receive the greatest of service but his first half was limited to one drill wide of the far post after holding off David Luiz and failing to get his head on Enner Valencia's driven cross.
Despite not creating many clear-cut chances there was a sense of foreboding about a Chelsea goal in the second half and after Jagielka almost gifted them one with a blind backpass which Stekelenburg only just managed to clear before being clattered by Costa, who was booked, it duly arrived with just over an hour gone.
Pedro collected the ball on the edge of the area, shifted it onto his left foot and fired a shot just under the crossbar - a goal worthy of winning any game.
Cahill made sure 12 minutes from time when he bundled home after Stekelenburg saved Hazard's low free-kick and substitute Willian added the third late on.
Source : PA
Source: PA