The result left the champions with four points from their opening five matches after their worse start to a season since 1988. Everton moved up to third in the table before the later matches.
Naismith replaced the injured Mo Besic and headed Everton in front in the 17th minute to complete a 19-pass move that cut Chelsea to ribbons.
The Scotland forward doubled Everton’s lead five minutes later before Nemanja Matic brought Chelsea back into the game with a superb 25-metre strike.
Chelsea failed to build on that goal, however, and Naismith wrapped up the points for the home side with another well-worked goal after 83 minutes, shooting wide of keeper Asmir Begovic who was replacing the injured Thibaut Courtois.
Leaders Manchester City visit second-placed Crystal Palace, Arsenal entertain Stoke City and Manchester United host Liverpool among games later on Saturday.