The climax ruined a spirited showing by Roberto Martinez's side, who matched their title-chasing opponents for prolonged periods of the game.
The decisive goal came from a set piece, as John Terry forced the ball in off Tim Howard.
Here's a look at some Everton-related talking points to emerge from this contest.
The first thing to note is that this was another impressive display from the Toffees, regardless of the score.
Roberto Martinez's side were full of energy, pressing their opponents high up the pitch and winning several key one-on-one matchups.
Seamus Coleman kept an in-form Eden Hazard relatively quiet while both centre-backs excelled. James McCarthy also produced one of his best displays in midfield, reducing the space for Chelsea's attacking midfielders.
While the home side recorded several shots on goal, half were forced from outside the box.
Everton also gained more control than the Londoners, dominating passing and possession numbers.
However, despite the positives, none of this returned any points—as the next slides will focus on.
Martinez selected a side to provide control, highlighted by the starts of Leon Osman and Steven Pienaar over Ross Barkley, Gerard Deulofeu or Aiden McGeady.
While this gave Everton an excellent foothold and a platform to play well—as it did against Tottenham Hotspur—it also meant there was a lack of penetration about the Toffees.
Occupying possession and building from the back will often slow the tempo in the final third, particularly against the top teams.
Chelsea were predominantly set and prepared for attacks, meaning the visitors became predictable and struggled to create enough opportunities. The Toffees were also far too conservative in the final third.
Despite passing more and enjoying more time on the ball, Everton recorded just eight chances to Chelsea's 14. As the game progressed, set pieces and individual brilliance seemed the only realistic route to goal.
Martinez kept his more direct options back for the final half hour, either expecting a lead or predicting a late Chelsea onslaught.
In theory, this should have provided far more of a threat than it did, with McGeady, Deulofeu and Barkley all introduced late on. Yet, despite this serious attacking potential, Everton's attacking play wilted during the closing stages.
Part of this was due to Ross Barkley's limited production.
The youngster emerged with a half-hour to play, tasked with initiating counter-attacks at pace.
Let down by a sluggish touch, a lack of awareness and some delayed anticipation, he struggled to make an impact, leaving several key opportunities wasted.
He failed to make any impression of note, making just 17 touches in 27 minutes, losing the ball three times and connecting just six successful passes.
For all his brilliance at the start of the season, Barkley's appeared severely short of form on his return from injury. This error-strewn showing was one of his worst contributions and will be a concern for his manager.
Another reason Everton huffed and puffed without ever being incisive was the lack of a genuine striker.
Lacina Traore hobbled off during the pre-match warm-up, leaving Steven Naismith as the sole forward, with little else on the bench.
Naismith was actually impressive in his link-up play, creating three of the Toffees' eight chances. However, he was never on the end of a move himself, spending more time interchanging with those behind him.
Without a constant presence in the final third, Everton had no focal point and nobody to look to for a final killer pass. This added to the declining tempo and lack of aggression once in the final third.
Traore's latest injury will make the decision to sign him and release Nikica Jelavic a little harder for some to accept. It's difficult to believe the Toffees would have lost both Chelsea and Tottenham games playing with a recognised striker.
Roberto Martinez has already highlighted his dislike for set pieces, as The Liverpool Echo's Greg O'Keeffe highlights.
However, as several sides have recently proved—such as Liverpool—they can also prove the difference in close contests.
The Toffees have still scored just once from a corner under Martinez, having found the net six times last season. At the moment, routines seem slow, disorganised and rarely carry as much threat as in previous years.
Another eight corners came and went during this game, with several other dead-ball opportunities wasted.
Martinez's stance is understandable, but set pieces are still an important avenue to goal, especially in crunch games against top sides. Numerous results have come via to a set piece strike, such as the Toffees' 1-0 win over Manchester United last season.
This is an area where Everton must improve, especially with the quality of delivery at the club.
Chelsea's winning strike only emphasises the point further.
This defeat effectively spells the end of Everton's Champions League challenge.
If key losses at Liverpool and Tottenham didn't terminate their chances, a third Premier League defeat in four games almost certainly has.
By the end of the weekend, the gap between the Toffees and the top four is likely to be in double figures, with just 12 games to go.
Instead, priorities must now turn elsewhere.
A top-six finish must be targeted—which is still an impressive feat in Martinez's first season—while the FA Cup tie with Arsenal gathers even more significance.
Statistics via WhoScored.com