Jose Mourinho’s side were two goals to the good inside the opening three minutes as Diego Costa found the net with just 35 seconds on the clock before Branislav Ivanovic doubled their lead against the shell-shocked hosts.
Kevin Mirallas’ fine header brought Everton back into the game just before the interval and they started the second half strongly before Eden Hazard’s driving run saw Seamus Coleman deflect the ball beyond Tim Howard.
The two teams then traded goals like heavyweight boxers going toe-to-toe, with Steven Naismith, Nemanja Matic, former Chelsea striker Samuel Eto’o and Ramires all finding the net in an astonishing eight-minute spell.
With Everton pushing forward in a desperate attempt to close the gap again, substitute Muhamed Besic’s dismal first touch allowed Costa to claim his second of the game and cap an all-time classic of the Premier League era.
Bizarrely it could have been even worse for Everton, as goalkeeper Howard could easily have been sent off for handling outside his area after just eight minutes.
Up until Naismith's strike, Chelsea appeared to have everything under control, with Costa showing the new attacking edge which was lacking from Mourinho's side last season.
It took just seconds to dismiss fears over a suggested hamstring injury as he scored before Everton had even touched the ball from kick-off.
There has been plenty of debate about some of the sums being spent by English clubs in the current window, but Costa is already looking value for money after scoring with his third shot on target this season.
The Brazilian-born Spain international was a constant menace, lurking with intent on the shoulder of the last defender and regularly capitalising on Everton's inability to play an offside trap which cost them two goals inside 170 seconds.
But for all the 25-year-old's threat, he still needs someone to provide the ammunition and that person is currently Cesc Fabregas, who more often than not found his compatriot with unerring accuracy.
The first goal game from exactly that source, as the former Arsenal and Barcelona midfielder threaded through a pass, catching the defence on their heels, for Costa to stride on to and dispatch past Howard.
In doing so he became only the second Chelsea player to score in his first three Premier League appearances for the club after Adrian Mutu.
More madcap defending saw last man Leighton Baines push out a fraction too slowly to make it obvious Ivanovic was offside - which he fractionally was - and the Serbian finished with the poise of a striker.
Such was the disbelief around Goodison even the electronic scoreboard took a couple of minutes to register the second goal, and Howard looked equally confused when he came clearly two yards outside his area to catch a through-ball before falling back inside the box.
A red card then would have ended Everton's afternoon, but Sylvain Distin's goal disallowed for offside after he followed in Romelu Lukaku's header against the crossbar suggested there was still fight in Roberto Martinez's side.
That materialised through Mirallas' glancing header from Coleman's cross, which was the first time Everton had got around the back six Chelsea had employed since going ahead so early.
Costa, put through again by Fabregras, was denied only by the outstretched leg of Howard before Hazard's cross from the byline was turned in by Coleman.
But the game was far from over as a brilliant run by Lukaku took three defenders away with him to allow Aiden McGeady to pick out Naismith in space and make it 3-2.
Matic's strike then deflected in off Jagielka before Eto'o, who signed a two-year deal in the week, headed in Baines' free-kick within six minutes of coming off the bench.
Ramires' one-two with Matic provided Chelsea's crucial fifth and, after Mirallas volleyed against the post, Costa added his second in the 90th minute when substitute Besic, making his debut, fluffed a backheel in the centre-circle which presented the Spain international with a run on goal after great work from John Obi Mikel.
People talk about the Spanish league being more technical, but when you see a game like that – blood, thunder, mistakes, great goals, individual performances – it had absolutely everything as a spectacle. You have had pure value for money whether you were at Goodison Park or watching that at home. A fantastic football match.
Diego Costa is a game changer and people like that are what you pay the big money for. They lost David Luiz and brought in him and Fabregas for only £10million difference – and what piece of business that is.