The visitors began with two goals in the first three minutes, but things unthinkably became even more chaotic after the break with five inside 11 minutes as both defences appeared to fall apart in the maelstrom, with the game eventually finishing 6-3.
Bizarrely it could have been even worse for Everton, as goalkeeper Tim Howard could easily have been sent off for handling outside his area after just eight minutes.
Conceding an early deficit ultimately cost the hosts, as Jose Mourinho's side went top of the Premier League, somewhat ironically after conceding three, on goal difference.
It had looked plain sailing after Diego Costa made it three goals in three matches since his £32million move from Atletico Madrid and Branislav Ivanovic's disputed second.
Kevin Mirallas' brilliant header on the stroke of half-time gave the hosts hope, only for Seamus Coleman's own goal to hand the initiative back to Chelsea as the madness began.
Steven Naismith and Nemanja Matic traded goals before substitute Samuel Eto'o made it 4-3 against the club he left in the summer, only for Ramires to give Chelsea breathing space again and Costa to add a late second.
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 35 seconds to dismiss fears over a suggested hamstring injury by scoring 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 bafflingly 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 Eden 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 Muhamed Besic, making his debut, fluffed a backheel in the centre-circle which presented the Spain international with a run on goal.
Source : PA
Source: PA