The Scottish international headed home the winner in first-half added time, his goal kick-starting the Roberto Martinez era at Goodison Park after three successive draws left the Spaniard with some convincing still to do.
In Mourinho's first spell in charge in 2004 he began with four successive wins and no defeat until his ninth league outing. This time around it seems he is not so special, with two wins, a draw and now a beating.
The much-anticipated Premier League debut of Chelsea striker Samuel Eto'o did not go to plan: he was outshone by Gareth Barry's first appearance for the Toffees after his deadline-day loan from Manchester City.
The class of Eto'o is not in doubt but the former Barcelona and Inter Milan forward may be rusty after a money-spinning spell in Russia.
It certainly looked that way when he headed Ramires' cross wide after five minutes. The Cameroonian then ballooned a long-range shot into the upper tier of the Gwladys Street end.
Still Everton could only offer Nikica Jelavic's weak header and Naismith's cross-shot, palmed away by Petr Cech, in the opening half-hour.
Martinez's preference for them to play out from the back almost cost them a goal when keeper Tim Howard tried to pass square from his six-yard box. He found only Schurrle, who cut back for Eto'o to shoot into an open goal.
Barry slid in with perfect timing to deflect the ball behind. The England international's positioning, reading of the game and calm under pressure gives the Toffees a first-rate shield for the back four.
Chelsea cranked up the pressure before the break with Howard saving Ramires' shot from an Eto'o pass, Schurrle firing over after Ramires' run and Branislav Ivanovic heading over.
But with half of an added minute left Osman crossed to the far post. Jelavic kept the ball alive and Naismith bundled home a header from close range.
Chelsea's tempo went up a notch after the interval and 60 seconds in Ramires played in Schurrle, who clipped over Howard into the side-netting.
Martinez brought on his £13 million signing from Wigan James McCarthy to shore up the midfield at the expense of Jelavic with 25 minutes to go. Chelsea threatened but then seemed to lose their way. David Luiz was booked for pulling down Mirallas.
Naismith departed to the dugout to a standing ovation to see Leighton Baines's 90th-minute free kick clip the angle of post and crossbar.