The Toffees looked destined for their first defeat in seven Premier League games when the former Leeds striker, on as a substitute, fired over Jussi Jaaskelainen deep into injury time.
Ivan Klasnic had come off the bench to give Bolton the lead 11 minutes from time and worse followed as Marouane Fellaini was sent off for kicking Paul Robinson.
The Belgian, returning to the side after four games out, could have few complaints as frustration appeared to be getting the better of Everton.
The hosts had squandered a number of chances to take the lead, many of them through the returning Louis Saha, as manager David Moyes' complaints about a lack of goals again rang true.
But Bolton, who also hit bar through Matt Taylor moments before Klasnic's effort, could not hang on for a win that would have taken them fifth.
The visitors had twice caused anxiety in the Everton defence early on, first as captain Kevin Davies broke the line to reach a long ball and Johan Elmander forcing Sylvain Distin to block.
Everton's first opportunity fell to Diniyar Bilyaletdinov, surprisingly preferred to Seamus Coleman, but the Russian skewed his shot well wide.
Bilyaletdinov had another chance as Leighton Baines found him six yards out with a fine cross but he failed to connect with his volley.
Elmander put a simple header wide from a similar distance after Taylor headed a corner back across goal.
Saha, on his first start since August, showed great skill to beat Robinson on the edge of the box but the Frenchman shot straight at Jaaskelainen.
Bilyaletdinov had a good shooting chance after being fed in the box by Steven Pienaar but lost momentum by cutting inside onto his left foot and Bolton recovered.
Saha had two shots cleared off the line in quick succession as Everton put the Bolton goal under more pressure.
The first chance came after Jaaskelainen failed to claim a Phil Neville cross but Gretar Steinsson blocked at point-blank range.
Saha then rose to meet the resulting Mikel Arteta corner but Lee Chung-yong volleyed out from under the crossbar.
Elmander inadvertently set up Fellaini when he trick to flick away another Everton corner but the Belgian blasted over the bar.
Bolton made the initial running after the restart and had the first chance as Davies headed forward and Lee squared for Elmander but the striker's first-time shot was deflected wide by Baines.
That resulted in the first of three Bolton corners in quick succession.
The visitors again went close from the second of them as Stuart Holden met Taylor's cross with a glancing header but Tim Howard clawed the ball out.
Everton responded as Bilyaletdinov drove at Jaaskelainen from 20 yards and Baines had a shot sliced narrowly over his own bar by Gary Cahill.
Zat Knight then got in Saha's way to deny the former Manchester United striker once again after good control on the edge of the box.
Moyes brought on Coleman, one of the stars of Everton's recent good run, for the frustrating Bilyaletdinov after 66 minutes.
The Irishman immediately looked a threat as he charged at the Bolton defence and cut inside but Jaaskelainen was not tested by his shot.
Holden required treatment after a kick on the ankle from Fellaini but recovered to take the corner which almost saw Bolton break the deadlock after 75 minutes.
The American picked out Taylor with his cross but the midfielder's header glanced the bar and went behind.
Bolton then grabbed the initiative as Taylor broke from deep down the right and sent over a bouncing cross for Klasnic.
With the defence frantically back-tracking, Klasnic inched ahead and just got his body to the ball to divert it in at the far post.
Everton's frustrations then started to get the better of them as Fellaini went down in a challenge from Robinson and responded by kicking out.
Referee Phil Dowd pointed the Belgian in the direction of the tunnel as Everton's night threatened to end in misery.
But Everton had one last throw of the dice and late substitute Beckford chose the perfect moment to score his first league goal for the club, chipping in from the edge of the box in time added on.
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