Chelsea failed to pip Liverpool to the Barclays Premier League top spot at Christmas and finished the game with 10 men after their skipper John Terry was sent off.
It all went wrong for the Stamford Bridge side, who had been expected to claim the victory at Goodison Park which would have seen them reclaim top spot in the table.
But from the moment Terry was sent off in the first half for a high tackle on Leon Osman, the best-laid plans of the west Londoners were in tatters.
Everton deserved their point, and thought they had won it with a disallowed Steven Pienaar effort near the end.
But Terry's absence had swung the game Everton's way as they ended Chelsea's 100% away league record this term.
Full-back Tony Hibbert returned to the Everton starting line-up for the first time since mid-October following a groin injury, allowing skipper Phil Neville to return to a midfield role.
That was the only Everton change from the side which won away to Manchester City last time out, with the injury-hit Merseysiders again using Tim Cahill as a lone striker.
Chelsea retained the side held at home by West Ham last week, manager Luiz Felipe Scolari resisting the opportunity to use both top scorer Nicolas Anelka and Didier Drogba in the starting line-up for the first time this season.
Even Everton die-hards were not expecting a shock result, and Chelsea's first attack had an ominous look about it. The ball fell for Ashley Cole on the corner of the box, and his drive deflected off Hibbert and gave Tim Howard a difficult, acrobatic save to make.
But Everton were able to produce some neat movement with their enforced line-up. Cahill, dropping deep, worked well as he interchanged position with Marouane Fellaini.
Chelsea goalkeeper Petr Cech was forced to deal with a dipping Mikel Arteta free-kick, while two Osman crosses from the right created opportunities for Cahill and Fellaini in the box.
But slowly Chelsea began to take control, maintaining possession with crisp passing as they forced Everton back.
Anelka hit a post from close range, but was adjudged to have handled in the build-up. Chelsea had a firm grip on proceedings, but the game changed dramatically after 36 minutes when Terry was red-carded.
Referee Phil Dowd was no more than 15 yards from a Terry challenge that was high and caught Osman on the ankle. In the current climate, the official probably felt he had to act decisively.
Terry was damned because he lunged in, and his foot - and the connection with Osman - was off the ground.
Terry's last red card for a foul on Manchester City striker Jo was rescinded but he is unlikely to be so lucky this time. He is now set to miss the Christmas matches against West Brom and Fulham, plus the FA Cup tie with Southend.
Chelsea were predictably furious, and in the minutes after the flashpoint, Frank Lampard and Ashley Cole were booked for dissent.
Chelsea sent on defender Branislav Ivanovic for Joe Cole at the break, while Drogba replaced Anelka.
Everton, though, must have felt that this was the best chance in eight years to register a win against the Stamford Bridge club.
But they needed to be more adventurous. Two minutes into the second period they were just that when Fellaini got on the end of a long Hibbert pass to test Cech.
But then Everton lost defender Joseph Yobo, who limped off with what looked like a hamstring injury. Leighton Baines came on after 61 minutes, with Joleon Lescott moving to central defense.
Chelsea then had Michael Ballack booked after 68 minutes for insisting an Everton wall was not back 10 yards. Referee Dowd paced out the yardage, proved the German was wrong, and promptly produced a yellow card.
Cech had to hurl himself backwards to touch away a Hibbert cross deflected dangerously under the bar off Lampard. A minute later Cech was needed at his best again to touch over a Lescott header.
Baines then fired in a low cross from the left, and Fellaini's flick went just wide of the far post. Arteta then curled a free-kick just over the bar.
Everton were denied a goal with six minutes left when Cech touched away an Osman shot from Fellaini's cross. The goalkeeper managed to get his hands on to the ball as it rolled towards the line, seconds before Steven Pienaar arrived to bundle the ball home.
Referee Dowd ruled out the goal, deciding that Cech had control of the ball before it was kicked out of his hands.
Chelsea sent on Wayne Bridge for Deco with two minutes left, keen now to secure a point which left them one behind Liverpool at the summit.
