Cesc Fabregas and Alvaro Morata were on target as Chelsea showed their Premier League pedigree by swatting aside Everton.
Fabregas fired Chelsea in front after 27 minutes and Morata headed in a second before half-time as the holders moved within three points of leaders Manchester United with a 2-0 win at Stamford Bridge.
Everton offered little to show that they could win at Chelsea for the first time in the league since 1994, a run which now spans 23 matches.
Chelsea, champions in May, lost on the opening day to Burnley, prompting suggestions of crisis, with head coach Antonio Conte seeking further squad strengthening and striker Diego Costa in exile.
Two weeks and two games later, Chelsea have beaten two sides with high aspirations for this season. And the four remaining days of the summer transfer window could see the Blues' augment their squad.
The victory over Tottenham at Wembley was followed up by a convincing win over Everton, who were second best throughout.
However, Sky Sports' decision to broadcast the West Brom v Stoke City game appears to have ruffled a few feathers.
Chelsea are the champions and their game isn't being shown on British tv on a Sunday. No one cares about them for real. Its on Chelsea TV— Hamez Rodriguez (@MrTund) August 27, 2017
Should sue sky sports for false advertising....— PC (@PC31878) August 27, 2017
Super Sunday....West Brom v Stoke????
No Chelsea v everton😐
For those who did see the game, they welcomed back Fabregas, back from a one-match suspension, and Pedro who returned in place of Andreas Christensen and Tiemoue Bakayoko.
And both Spaniards were influential. Pedro's pace and movement tested the Toffees and Fabregas' guile proved instrumental with N'Golo Kante dominating midfield.
Wayne Rooney, concentrating on domestic duty following his international retirement, cut a frustrated figure at times as he tried to rouse the Toffees, who might have been reduced to 10 men inside 10 minutes.
Idrissa Gueye was booked after his studs met Fabregas' shin, but the card could have been red.
Chelsea had a flurry of chances. A Pedro overhead kick went over. Willian had a deflected effort clear the target and Jordan Pickford saved from David Luiz and then Pedro.
Everton were holding firm, but then Fabregas found an opening.
Willian, on the right, played the ball in for the Spaniard, who played a one-two with Morata. The return reached Fabregas at the second attempt after a ricochet off Ashley Williams and he struck the ball on the volley inside the far post.
Gylfi Sigurdsson, who scored spectacularly on Thursday against Hadjuk Split, dragged an effort wide across goal as Everton made a rare foray forwards, but soon afterwards it was 2-0.
Morata went down inside the area and Williams remonstrated with him before offering a hand to help him up.
That offer was withdrawn when Williams realised Chelsea were still on the attack after Everton failed to clear as Kante applied pressure.
Next Victor Moses went down on the edge of the box, but referee Jonathan Moss played advantage.
The ball broke for Azpilicueta, who had time to cross and Morata had space to send a free header in. Everton's defenders were too busy appealing for offside to mark Morata.
Mo Besic replaced Tom Davies at half-time as Everton sought a midfield foothold.
Sandro Ramirez should have done better when found by Wayne Rooney, but Antonio Rudiger covered the danger.
The first-half order was soon restored as Chelsea pushed the visitors deep into their own territory.
Pedro fired narrowly wide and then Moses weakly shot at Pickford when he had time to pick his spot.
Rooney mishit a volley and was booked soon afterwards for dissent as another Everton attack disintegrated.
Williams hooked an effort on to the roof of the net as Chelsea struggled to clear an Everton free-kick and the defender next headed a Rooney cross wide.
Gueye came close soon afterwards, but Chelsea's defence would not be breached as they recorded a first clean sheet of the season.