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Ancelotti faces a nervous wait to discover if he will retain his job after failing to win a trophy in his second season at Stamford Bridge and this was a suitably downbeat end to a frustrating campaign.
Despite having Seamus Coleman sent off for a second booking in the second half, Everton sunk the Blues when Beckford hit a superb winner in the 74th minute.
Aside from a John Terry shot which hit the post, Chelsea did little to excite their supporters with £50 million Fernando Torres again a forlorn figure.
Chelsea still finished second ahead of Manchester City on goal difference but they were nine points behind champions Manchester United.
The travelling Blues fans were at their most vocal when chanting their backing for Ancelotti, making clear they want the Italian to stay on.
But, just a year after winning the double, speculation is rife that Ancelotti will suffer the sack when he meets Chelsea owner Roman Abramovich in this week.
Everton always looked more lively and Phil Jagielka went close when he met Mikel Arteta's cross with a firm header which clipped the top of the bar.
Coleman was then denied in front of goal by a fine Ashley Cole tackle and it was not until the 24th minute that Chelsea created a serious chance as Torres and Frank Lampard combined to set up Nicolas Anelka but Sylvain Distin slid in to block.
Tim Howard was tested for the first time in the final minute of the first half when the Everton goalkeeper saved twice from Anelka.
Coleman was sent off early in the second half. He appeared to win back the ball as he dived into a challenge but referee Peter Walton was unimpressed with the studs-up tackle.
After a fracas involving several players from both sides, Coleman was shown the red card.
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 Beckford brilliantly controlled a long ball inside the Chelsea box and turned inside Alex but Petr Cech smothered his shot.
Beckford was not to be denied and took centre stage in magnificent style to secure victory with 16 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 Paulo Ferreira but he took full advantage as he continued his charge.
Cech came out to meet him as he raced into 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.
