Cesc Fabregas broke Everton's resistance by coolly clipping into the bottom corner from Alvaro Morata's instinctive knockdown, ending a smart move that began with a quick free-kick.
Morata's thumping header doubled Chelsea's lead before the break, the Spaniard gleefully finishing from Cesar Azpilicueta's perfect cross.
Everton did not get a sight of goal until Sandro's poor scuffed shot was deflected wide shortly after the break, a move that was only started by Azpilicueta's mistake.
In truth, Chelsea really ought to have scored more; Victor Moses shot straight at Jordan Pickford when played through, and Pedro drove just wide after nutmegging Gylfi Sigurdsson on the edge of the box.
The Toffees, playing their third tricky away game in seven days, have now failed to win in their past 23 league matches at Stamford Bridge.
For Chelsea, this was the perfect follow-up to last weekend's impressive victory over Tottenham at Wembley.
After suffering a shock defeat by Burnley on the Premier League's opening weekend, Chelsea needed a performance that was more in tune with the home form of last season's title win.
They got it. Right from the outset there was an intensity to their passing, movement and pressing that was only matched by the animated Antoino Conte's cajoling on the sidelines.
Everton, perhaps fatigued having followed their draw at Manchester City on Monday with Europa League progression at Hajduk Split on Thursday, could not hold them back for long.
Morata was the only Chelsea player on the pitch who had been slow to make an impression, but he reacted impressively, after Ashley Williams blocked his initial pass, to set up Fabregas perfectly for a richly deserved opener.
The former Real Madrid striker looked to be struggling with the physicality and pace of the opening stages, but in scoring his header he became the first player in Premier League history to both score and assist a goal in each of his first two home games.
The reigning champions of England's top division have never lost their opening two home fixtures of a top-flight season, and by the time Morata was roundly applauded as he was replaced by Michy Batshuayi, Chelsea were heading for a straightforward victory.
Three away games in seven days was never going to be easy, no matter the opposition, but Everton barely troubled Thibaut Courtois. It wasn't until the 87th minute that Chelsea's keeper was forced into making a save - from Idrissa Gueye's shot that appeared to be going over the bar.
Having been soundly outplayed in the first half, the second period felt more like damage control.
Muhamed Besic, whose father was shot in his native Bosnia on Saturday, replaced the disappointing Tom Davies at the break, but Aaron Lennon, making his first league appearance since February, had more impact from the bench.
His cross caused momentary panic in a Chelsea box that had seen very little action, before Williams glanced just wide from Sigurdsson's cross in the closing stages.
There were positives - notably Mason Holgate's composed display after his mistake at City on Monday - but Everton are clearly still feeling the absence of Romelu Lukaku.
Wayne Rooney, Sigurdsson and Sandro never really combined convincingly, and Rooney appeared to let frustration over a first-half Marcos Alonso challenge affect his game.
The 31-year-old was finally shown a yellow card for dissent towards the end of a game he and his team-mates will want to forget.
The Toffees have never won a Premier League game in which they've been two or more goals behind at the break, a run that now stretches into four draws and 55 defeats.
Chelsea boss Antonio Conte told BBC Sport: "We must be pleased with the performance. We played a really good game. We dominated and had plenty of chances.
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"The only negative thing is we should be more clinical. But there were a lot of positive things.
"There are maybe four or five days to go before the close of the transfer market. I think the club is trying to work very hard to improve the squad. I need to rotate my players - for that I need a good number of players. I'm sure the club are trying to do their best."
Everton boss Ronald Koeman told BBC Sport: "The quality of our opponent made it really tough, but I'm still disappointed at our first half. I was proud of how we fought until the end. We made a lot of mistakes in the first half. They were more aggressive.
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"If you have a few games in a short amount of time with a lot of travelling, it's hard to do with 11 players. We need a striker more to bring in. Sandro needs to adapt to the Premier League. Dominic Calvert-Lewin is only 20. You can't do a whole tough season with different competitions, you need one more striker."
Chelsea next play in the Premier League away to Leicester on Saturday, 9 September (15:00 BST), after the international break.
Everton also next play in the league on 9 September, at home to Tottenham (15:00).
Match ends, Chelsea 2, Everton 0.
Second Half ends, Chelsea 2, Everton 0.
Attempt saved. Willian (Chelsea) right footed shot from the right side of the box is saved in the bottom right corner.
Substitution, Chelsea. Andreas Christensen replaces Victor Moses.
César Azpilicueta (Chelsea) is shown the yellow card for a bad foul.
Foul by César Azpilicueta (Chelsea).
Aaron Lennon (Everton) wins a free kick on the left wing.
Corner,  Everton. Conceded by Marcos Alonso.
Attempt blocked. Idrissa Gueye (Everton) right footed shot from outside the box is blocked. Assisted by Aaron Lennon.
Attempt blocked. Aaron Lennon (Everton) right footed shot from the centre of the box is blocked. Assisted by Wayne Rooney with a headed pass.
Foul by Michy Batshuayi (Chelsea).
Leighton Baines (Everton) wins a free kick in the defensive half.
Corner,  Chelsea. Conceded by Muhamed Besic.
Attempt blocked. Marcos Alonso (Chelsea) left footed shot from outside the box is blocked. Assisted by Willian.
Attempt blocked. Michy Batshuayi (Chelsea) right footed shot from the left side of the box is blocked. Assisted by Cesc Fàbregas.
Attempt missed. Ashley Williams (Everton) header from the centre of the box is close, but misses to the right. Assisted by Gylfi Sigurdsson with a cross following a corner.
Corner,  Everton. Conceded by David Luiz.
Substitution, Everton. Aaron Lennon replaces Phil Jagielka.
Attempt missed. Ashley Williams (Everton) right footed shot from outside the box is just a bit too high. Assisted by Muhamed Besic with a headed pass following a set piece situation.
Foul by David Luiz (Chelsea).
Dominic Calvert-Lewin (Everton) wins a free kick on the left wing.
Attempt blocked. Tiemoué Bakayoko (Chelsea) right footed shot from outside the box is blocked. Assisted by Willian.
Foul by Marcos Alonso (Chelsea).
Idrissa Gueye (Everton) wins a free kick in the defensive half.
Substitution, Chelsea. Michy Batshuayi replaces Álvaro Morata.
Victor Moses (Chelsea) is shown the yellow card for a bad foul.
Foul by Victor Moses (Chelsea).
Leighton Baines (Everton) wins a free kick on the left wing.
Substitution, Chelsea. Tiemoué Bakayoko replaces Pedro.
Foul by N'Golo Kanté (Chelsea).
Muhamed Besic (Everton) wins a free kick in the defensive half.
Wayne Rooney (Everton) is shown the yellow card.
David Luiz (Chelsea) wins a free kick on the right wing.
Foul by Dominic Calvert-Lewin (Everton).
Attempt missed. Wayne Rooney (Everton) right footed shot from outside the box misses to the left. Assisted by Dominic Calvert-Lewin with a headed pass.
Attempt blocked. César Azpilicueta (Chelsea) right footed shot from outside the box is blocked. Assisted by Cesc Fàbregas with a cross.
Corner,  Chelsea. Conceded by Mason Holgate.
Pedro (Chelsea) wins a free kick on the left wing.
Foul by Muhamed Besic (Everton).
Antonio Rüdiger (Chelsea) wins a free kick in the defensive half.
Chelsea produced a dominant home performance to comfortably beat Everton for their second win of the Premier League season.