On a disappointing evening on Merseyside, we were unable to recover from falling behind right on the stroke of half-time, and though we began the second half brightly, we struggled to find a route back into the game.
Andre Schurrle had our best chance of the game just after the break, but his chipped effort rolled agonisingly wide of the post.
Attention now turns to the Champions League, and an opening game against FC Basel at Stamford Bridge on Wednesday.
Samuel Eto'o was handed his Blues debut by Jose Mourinho, with our new signing operating as a lone striker.
In defence, David Luiz, making his first start of the Premier League campaign, partnered John Terry, while there was also a first start of the season in midfield for John Mikel Obi.
Juan Mata, Eden Hazard and Schurrle were the trio tasked with supplying the ammunition for Eto'o.
For Everton, Gareth Barry, who recently joined the club on loan from Manchester City, started, while Romelu Lukaku, on loan from Stamford Bridge, was ineligible to play any part.
Chelsea fell behind inside the opening minute of last season's corresponding fixture, but we were first to threaten this time.
Ramires whipped in a delightful ball from the right-hand side, and though Eto'o connected, our new signing could only direct his header wide. Moments later a jinking Mata run was brought to a halt by a last-ditch challenge by Phil Jagielka.
The home side, who went into the game still searching for their first league win of the season, were next to go close. The ball was worked out wide to Naismith; his cross was a decent one, but Nikica Jelavic, who rose highest to meet the delivery, could only head down and safely into the arms of Petr Cech.
There was little to choose between the sides during the opening 20 minutes with plenty of neat, tidy passing, but a lack of a cutting edge in the final third.
Barry was fortunate to escape a caution for a scything tackle on David Luiz as he attempted to bring the ball out from the back, with the Brazilian looking to influence proceedings further up the field of play.
Just before the half-hour mark we were presented with a glorious opportunity to take the lead, and it owed much to a breakdown in communication in the Everton defence.
Sylvain Distin rolled the ball back to Tim Howard, but the goalkeeper, under pressure, saw his clearance land at the feet of Schurrle. The German showed awareness to lay it into the path of Eto'o, but as the striker fired towards goal, Barry had made up enough ground to make the block and divert the ball over the bar.
Moments later the hosts saw their best chance of the half go begging when Naismith shot wide from Mirallas's pull-back, and as the game began to warm up Howard saved well to deny Ramires.
We continued to create chances, and eight minutes before the break Schurrle should have done better when, with time on his side, he blazed high over the bar from a good position after a Ramires run had been brought to a halt.
Branislav Ivanovic then went close, heading narrowly over the bar from a Mata free-kick, but with virtually the last action of the first half Everton took the lead.
Leon Osman delivered a cross to the far post, and as Jelavic directed it back across goal, Naismith reacted quickest and headed past Cech from close range.
It was harsh on the Blues, and left Mourinho with plenty to think about at the break.
It was the Blues quickest out of the blocks after the restart as we looked to restore parity. Ramires, advancing from midfield, slipped a clever pass into the path of Schurrle, who dinked his effort over Howard, but with the net looking set to bulge, it dropped just the wrong side of the post.
It was a positive start to the second half, and moments later Howard struggled to hold a powerful Hazard strike from outside the box, and while Eto'o was first on to the loose ball his shot was tame and rolled wide.
Shortly before the hour mark, and sensing the need for a change, Mourinho made a double substitution, replacing Mata and Schurrle with Oscar and Frank Lampard, and the Brazilian was involved instantly, going down inside the box under a challenge from Osman. The referee, however, saw nothing in it and waved play on.
The introduction of the two substitutes saw Lampard move into midfield alongside Mikel with Ramires shifting out to the right-hand side and Oscar taking up a central role just off Eto'o.
It was Chelsea dominating in terms of possession but the Everton defence was standing firm. Fernando Torres was then introduced with 22 minutes left on the clock at the expense of Ashley Cole as Mourinho threw caution to the wind and went with three at the back.
Kevin Mirallas forced a smart save from Cech with a curling free-kick as Roberto Martinez's side attempted to put the game out of our reach, and as the match entered the final 15 minutes it was flowing from end to end.
Eto'o went close as he met a Ramires cross at one end, while at the other Cech pulled off another impressive save to deny Mirallas.
Hazard became the second Chelsea player to enter the referee's book 12 minutes from time when he tripped Seamus Coleman, who had worked himself into a dangerous position on the edge of the box, and we breathed a collective sigh of relief as Leighton Baines's subsequent free-kick came to nothing.
If anything, it was the home side looking more threatening late on, and Cech needed to be alert to save from Mirallas with his feet after the Belgian had got beyond Terry, which was soon followed by a Baines free-kick clipping the top of the bar.
Chelsea (4-2-3-1): Cech; Ivanovic, David Luiz, Terry (c), Cole (Torres 68); Ramires, Mikel; Schurrle (Lampard 57), Mata (Oscar 57), Hazard; Eto'o.
Unused substitutes:Schwarzer, Cahill, Essien, De Bruyne.
Booked Ivanovic 64, Hazard 79, David Luiz 82, Mikel 86
Everton (4-2-3-1): Howard; Coleman, Jagielka (c), Distin, Baines; Osman, Barry; Naismith (Stones 88), Barkley, Mirallas (Deulofeu 90+1); Jelavic (McCarthy 66).
Unused substitutes: Robles, Heitinga, Oviedo, Gueye.
Scorer Naismith 45