Beckford ran almost the length of the field after 75 minutes to end Everton's frustrating Barclays Premier League campaign on a high at Goodison Park.
Chelsea later revealed that Ancelotti had been sacked as manager.
Crowded out: Leon Osman (centre) tries to hold off Chelsea's Alex (left) and Branislav Ivanovic (right)
It was no more than the Merseysiders deserved for their dominance, even after Seamus Coleman was sent off fora second bookable offence early in the second half.
Chelsea, with their title challenge over and second place all but wrapped up, played without fight throughout.
Everton made most of the running and continued to dominate after Coleman saw red after a lunge at Jon Obi Mikel in the 53rd minute.
Close encounter: Mikel Arteta is shadowed by Chelsea's John Obi Mikel
Beckford's superb goal, his 10th of the season, was fine reward for a performance in which he had frustratedbut shown plenty of determination and flashes of brilliance.
He particularly tormented Alex in thesecond half and the Brazilian defender was fortunate not to become the game's second sending off.
Aside from a John Terry shot which hit the post, Chelsea did little to excite their supporters with ?50million Fernando Torres again a forlorn figure.
Taxi for Carlo: Ancelotti (right) could be on his way out of Stamford Bridge
Style and substance: Fernando Torres (left) shields the ball from the imposing figure of Everton's Sylvain Distin
The visiting fans were at their most vocal when chanting their backing for manager Carlo Ancelotti, making clear they want the Italian to stay on despite continuing uncertainty.
Chelsea clearly missed Didier Drogba,out with a groin injury, but Everton lacked their inspirational captainPhil Neville due to a painful mouth infection.
The match began at typical end-of-season pace with little urgency shown by either side in the opening five minutes.
Everton upped the tempo when Jack Rodwell broke down the right and pushed into the box to win a corner.
Phil Jagielka got forward for the resulting set-piece and went close when he met Mikel Arteta's cross witha firm header which clipped the top of the bar.
Coleman was then denied in front of goal by a fine Ashley Cole tackle and Leon Osman was denied a penalty after going down under a challenge from Alex.
It was not until the 24th minute thatChelsea created a serious chance as Torres and Frank Lampard combined to set up Nicolas Anelka but Sylvain Distin slid in to block.
Beckford should have done better whenhe broke into the area but his final touch was neither shot nor cross and Chelsea survived.
Off: Peter Walton gives Seamus Coleman his marching orders
Tim Howard was tested for the first time in the final minute of the first half when he saved twice from Anelka.
Beckford appeared to beat Alex early in the second half but was body-checked and the defender was booked.
The Merseysiders' afternoon took a turn for the worse as Coleman was dismissed.
The Irishman lost control but appeared to win back the ball as he dived into a challenge but referee Peter Walton was unimpressed with the studs-up tackle.
Final game? Carlo Ancelotti faces the sack
After a fracas involving several players from both sides, Coleman was shown the yellow and red cards but he still left to a standing ovation in recognition of an outstanding season.
That briefly sparked Chelsea into life and Terry went close to opening the scoring with a thunderous low shot from distance which struck the base of the post.
Everton quickly responded as Beckfordbrilliantly controlled a long ball inside the Chelsea box and turned inside Alex but Petr Cech smothered his shot.
Arteta then went close as he fired narrowly wide from the edge of the box.
Winner: Jermaine Beckford scored the only goal
Beckford continued to trouble Alex and Walton showed leniency when the defender brought him down again justinside the Everton half.
Alex was spared further punishment as Ancelotti replaced him with Paulo Ferreira moments later.Beckford was not to be denied and took centre stage in magnificent style to secure victory with 15 minutes remaining.
The former Leeds forward broke up a Chelsea attack on the edge of his own box and then set off on a long run into the other box.
He got a lucky break on halfway when the ball rebounded kindly off Ferreira but he took full advantage as he continued his charge.
Cech came out to meet him as he racedinto the box and the keeper got a hand to the ball as Beckford chipped for goal but the shot had just enough power and bobbled over the line.
It was just what the hosts deserved and Chelsea lacked the urgency to press for an equaliser.
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Explore more:People: Sylvain Distin, Phil Neville, Petr Cech, Didier Drogba, Ashley Cole, Phil Jagielka, Leon Osman, Fernando Torres, Frank Lampard, Nicolas Anelka, Carlo Ancelotti Places: Leeds