The Toffees were undone twice inside the first three minutes as first Diego Costa and then Branislav Ivanovic both found the net.
After that early shock Kevin Mirallas pulled one back for the hosts just prior to half time before the match exploded with five goals in a mad 10-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 toe-to-toe contest 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 probably served us well (in the) second half. Maybe we were too relaxed before that," Terry told Sky Sports.
"The way we kept responding was excellent and something that we didn't have last year so that delights me more than anything."
Terry was especially pleased to have triumphed at Goodison Park, where they lost 1-0 last year to a solitary Naismith goal.
"I think at times we drop points against the lesser sides and we've not done so well here in recent years so to come here and get the win in the manner we did was incredible," he added.
The Chelsea skipper also reserved special praise for Costa, who made it four goals in three matches since moving from Atletico Madrid in the summer.
He added: "He's been brilliant. I played against him in the Champions League and realised he was a top player but when you see him every day he's got everything and he's got off to a flying start with us and long may it continue because that was the difference."