The Toffees were undone twice inside the first three minutes as first Diego Costa and then Branislav Ivanovic both foiled half-baked attempts to play the offside trap by Everton's ragged back four.
After that early shock, Kevin Mirallas pulled one back for the hosts on the stroke of half-time before the match exploded with five goals in a mad 11-minute spell in the second half.
Seamus Coleman put through his own net before Steven Naismith, Nemanja Matic, Samuel Eto'o and Ramires all scored as Chelsea came out of the five-a-side-like shenanigans 5-3 to the good before Costa pounced to round off the win late on.
"It was disappointing to throw away the lead just before half-time, but we got the wake-up call and it served us well second half," Terry said. "The way we kept responding today was excellent and something that we didn't have last year so that delights me more than anything."
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 Costa made it three goals in three matches since his £32 million move from Atletico Madrid and Ivanovic's disputed second.
Mirallas's brilliant header on the stroke of half-time gave the hosts hope, only for Coleman's own goal to hand the initiative back to Chelsea as the madness began.
Naismith and Matic traded goals before substitute 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.
The Spaniard's performance, however, caused a post-match spat between Mourinho and his Everton counterpart Roberto Martinez. Mourinho accused Everton's players of trying to goad Costa, who was booked for an altercation with Coleman.
Mourinho said: "There is a good tradition with Everton teams because everything is positive: the manager, the quality of their football.
"But to be chasing cards to a player who once more had good behaviour and was just here to play football is disappointing.
"At the end of the story Diego is maybe the best player in the Premier League in the first three matches and he has two yellow cards; one against Burnley where he didn't simulate, it was a penalty, and today when everyone was chasing him to get him in trouble.
"That is disappointing."
Martinez's response was to suggest Costa's behaviour showed he had yet to learn the standards associated with English football but refused to be drawn into a slanging match.
"I am disappointed if a manager who has won a game away from home complains about the attitude of players," said the Spaniard.
"Foreign players who come to the Premier League need to understand the ethics and the culture of the British game.
"The last thing you want to see is disrespect from a player to another player and I am sure he will learn that very quickly."