There were few clear-cut chances of note in the opening exchanges, with Ross Barkley drilling a shot wide, before Zouma seeing his effort go over for the visitors.
But the game suddenly sparked in the 16th minute, as Steven Naismith headed past Begovic to give Everton the breakthrough.
The goal breathed life into the home side, and moments later Begovic had to be alert to deny McCarthy and Kone.
And, just 5 minutes after netting his first, Scotland international Naismith doubled his tally, fizzing a shot low into the bottom corner, to leave Jose Mourinho's team rattled, and extend the Toffees advantage.
But, the old saying is never write off champions, and Matic gave the Blues encouragement with a stunning goal in the 36th minute to make the score 2-1 and leave the contest finely poised at half-time.
Jose Mourinho made his first substitution of the game, bringing on Kenedy for Mikel in the second half, and the young Brazilian made an early impact, sending a shot wide, and Diego Costa then had a chance to equalise but delayed his shot and the chance was wasted.
This miss was to prove costly, as Naismith completed his hat-trick with 7 minutes remaining, to inflict more misery on Chelsea's start to the season, with the Blues now having picked up just 4 points from a possible 15.
Everton: 3 (Naismith 17, 22, 82)
Chelsea: 1 (Matic 36)
Match report by Joe Baker
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