In a game of very few chances the Toffees dominated possession following the sending-off but, with no fit strikers in the squad, the visiting back four never looked like conceding.
Chelsea pushed forward straight from the off pressuring Everton's back line and the 35,000 home fans were quickly silenced when a rasping Ashley Cole shot inside the first two minutes was palmed over the bar by Tim Howard.
With all four first-team strikers sidelined through injury midfielder Tim Cahill played as the lone frontman as David Moyes set out a 4-4-1-1 formation with Marouane Fellaini just behind the striker.
The home side refused to sit back and soak up the pressure from Chelsea, who had won every game away from home this season, and scrapped for every bit of possession. Cahill looked a handful for Terry and Alex at the heart of the visiting back four.
It was the sprightly Australian that carved out Everton's first chance after he battled for the ball just outside the box and slid a pass to Phil Neville who drilled a low effort from 25 yards but Petr Cech smothered it at the first attempt.
Moyes' men were not letting the Londoners settle on the ball and good width from Leon Osman on the right wing brought headers from Fellaini and Cahill inside the first 15 minutes but neither really tested Cech.
Chelsea started to keep the ball from the home side by impressively spraying the ball across the park through Deco and Frank Lampard and it was quick one-touch passing that opened up Everton on 25 minutes.
Wing-back Ashley Cole latched on to a Deco ball inside the box and had time to pick out a late charge from Nicolas Anelka but the French hitman saw his effort deflected wide.
The talking point of the game came just after the half-hour mark when Chelsea were reduced to ten men following a late challenge on Osman from Terry.
His desperate lunge brought a straight red from referee Phil Dowd after he missed the ball and his studs connected with Osman's right ankle.
Half time brought two changes from Chelsea boss Luiz Felipe Scolari who sacrificed Joe Cole for defender Branislav Ivanovic and also decided to swap Anelka with Didier Drogba.
Everton started the second half as they finished the first and were almost playing with four up front with Steven Pienaar and Osman getting down the wings.
A high floated cross from Tony Hibbert on 51 minutes found the head of Fellaini who managed to get in between two Chelsea players but his effort didn't have the power to trouble Cech.
The home side were throwing wave after wave of attack at the visitors but, despite being camped deep inside their own half, Chelsea were not giving away any clear chances and Everton had to settle for a string of corners and long-range efforts.
With very few efforts testing either keeper it was Cech that was eventually called into action when a cross from Hibbert on 75 minutes deflected high off Lampard's back and looked to be looping over Cech's head but the lanky shot-stopper managed to arch his back and touch the ball over the bar.
The Chelsea number one pulled off another match-saving stop from the resulting corner after Mikel Arteta had swung the ball on to Joleon Lescott's head but he reacted well to palm the ball away from the top corner.
Everton were forced into making a change when Joseph Yobo pulled up with a hamstring problem but his replacement, Leighton Baines, almost had an instant impact when he whipped in a low 80th-minute cross for Fellaini but his back-heel flew inches wide of the post.
Everton thought they had scored with only minutes remaining after a low Osman drive inside the box looked to have been spilled by Cech on the goal-line but, with Pienaar having bundled the ball over the line, his celebrating was cut short after a flag was raised for offside.