The visitors triumphed thanks to two long-range scorchers from Frank Lampard and Didier Drogba, but neither team ever really had a grip on this game.
Chelsea began the sharper of the two teams, with the tricky Arben Robben looking to cause trouble for the home defence.
The Dutchman set up fellow frontman Drogba in the left channel and the Ivory Coast man sent a warning shot across Tim Howard's bows in the eighth minute.
The home team were struggling to clear their lines against the visitors' onslaught in the early stages and looked vulnerable to a counter-attack when they did venture forward.
The Goodison crowd were incensed in the 17th minute, as referee Mark Halsey waved away claims by Andy Johnson that he had been fouled by the advancing Henrique Hilario.
Jose Mourinho did nothing to calm the ire of the Toffees support by calling for Johnson to be booked for diving.
This fired up the Merseysiders and they began to tie up more Chelsea resources at the back.
Mikel Arteta put in several useful crosses, but Hilario was more often than not first to the incoming ball.
Johnson and the newcomer Victor Anichebe were forging a useful working relationship as neat interplay started to pay off.
And it was the 18-year-old who helped to give an emboldened home team the lead when he was bundled over in the box.
It was neat lay-off by Johnson which found Anichebe bursting into the box, before he was dragged down by Khalid Boulahrouz's overzealous marking.
Referee Halsey awarded the penalty and it fell to Arteta to send keeper Hilario the wrong way from the spot on 38 minutes.
It would be wrong to rest on your laurels against the millionaires of Chelsea and Mourinho sent his team out with renewed purpose after the break.
And it only took four minutes after the interval for Everton to surrender their hard-fought lead to a well-taken free-kick.
Lee Carsley was adjudged to have handled the ball in a midfield melee 25 yards out and Michael Ballack sent a right-footed curling dead-ball narrowly past Tim Howard's outstretched palm.
It clipped the post before nestling in the Everton net via Howard's back, leaving the home support stunned after their first half endeavours.
Back in the game, the Stamford Bridge outfit went out on a rampage and nearly took the lead when substitute Salomon Kalou thundered his shot against the woodwork in a goalmouth scramble.
But again, Everton stopped them in their tracks with a well taken corner on 64 minutes.
Arteta had already put in a well placed free-kick and corner into the Chelsea before his third dead-ball was met by centre-half Joseph Yobo.
He rose above a crowd of players to send the ball into the roof of the net, Everton's resilience putting them back into the driving seat.
But Chelsea finished with two superb pieces of skill, first Lampard hit a right-foot shot from the left edge of the area which dipped wickedly under Howard's crossbar.
And then Drogba hit an amazing half-volley from 30 yards on 87 minutes to leave Everton with nothing to show for their efforts.