Everton celebrate James Vaughan's late opener for Everton
By Les Roopanarine
Everton struck at the death to win at home for the first time since September and condemn 10-man Burnley to a ninth successive league game without a win.
Substitute James Vaughan turned home a Marouane Fellaini cross from close range with seven minutes remaining.
Steven Pienaar then sealed the win in injury time after being fed by Yakubu.
David Nugent hit the post for Burnley, but the turning point for the Clarets came when Stephen Jordan saw red for a second bookable offence on the hour.
Everton's victory, their first in the league since early November, ends a winless streak at Goodison Park stretching back to mid-autumn, when Blackburn were on the receiving end of a 3-0 defeat.
More importantly for manager David Moyes, who could only watch with mounting dismay when his side's early-season lethargy was compounded by a wholesale injury crisis, Everton now lie 11th in the league table, five points clear of the relegation zone.
Moyes pleased with Everton performance
Having previously picked up just a solitary point on their travels, Burnley arrived on Merseyside with the worst away record in the division, but a battling performance belied that discouraging statistic.
Burnley gave a decent account of themselves throughout, so much so that - despite Everton's numerical advantage - the outcome remained in the balance until the dying minutes.
The Clarets' best chance came shortly after the break, when Nugent struck the woodwork from a tight angle after a half-cleared Chris Eagles corner received a useful touch from Wade Elliott.
Owen Coyle's decision to name an unchanged Burnley line-up held special significance for Nugent, handing the lifelong Everton supporter a longed-for chance to play at Goodison Park for the first time.
Nugent endeavoured to make the most of the opportunity, capitalising on an early defensive error by Lucas Neill to shoot wide from a tight angle and later failing narrowly to reach an inviting deflection off Tony Hibbert.
But Jordan's red card necessitated a tactical reshuffle by Coyle, bringing a premature end to Nugent's afternoon when he was replaced just after the hour by defender Christian Kalvenes.
First goal was offside - Coyle
As for Everton, their cause was hardly advanced by the absence of top-scorer Louis Saha, who was ruled out by a hamstring injury.
In the Frenchman's absence, Yakubu - making only his third start of an injury-blighted campaign - proved a capable deputy.
Two early penalty claims by the big Nigeria international, who thundered a shot against Mike Duff's hand from point-blank range before going down under pressure from the Northern Ireland defender, smacked of optimism.
But there was nothing speculative about the cushioned volley with which Yakubu shuddered Brian Jensen's post midway through the first half.
Leon Osman, Pienaar and Diniyar Bilyaletdinov, who drew a stretching one-handed save from Jensen after being fed by Pienaar, likewise threatened for Everton before the interval, but their incisive build-up play was too often undermined by a lack of cutting edge.
With the hour-mark approaching, what had initially been an open and entertaining game was threatening to fade into mediocrity.
But the dismissal of Jordan, who received a second yellow card for a senseless and prolonged tug on the shirt of Pienaar, reignited proceedings, providing the cue for a sustained Everton onslaught.
Fellaini went close from a Baines free-kick before a deflection off the towering Belgium international sat up kindly for Yakubu, whose looping header forced a fine tip-over from Jensen.
Burnley's lack of numbers forced them into a strong rearguard action, but just as it seemed that the afternoon would end in frustration for Everton, up popped Vaughan.
With seven minutes remaining, a Pienaar back-flick reached Fellaini. His centre was missed by Yakubu but reached Vaughan at the far post, and the injury-plagued youngster slotted home for his first goal in two years.
Deep into injury time Yakubu cut in from the right to feed Pienaar, who gleefully fired in to complete a miserable afternoon for Burnley.
Everton will be buoyed by the victory but, as the new year dawns, Burnley - who stand just three points clear of the relegation zone - face the very real prospect of being drawn into a fight for Premier League survival.
Everton manager David Moyes on James Vaughan:
"I am really pleased for James, who has had a terrible time with injuries for more than two years.
"This time he has come back without even a reserve run-out.
"He has missed much of his development, so we are just trying to nurse him through to get him back to what he was like as an outstanding teenager."
"We played really well in the first half but didn't get the goal our play merited.
"But overall we deserved the victory.
Burnley manager Owen Coyle on Everton's first goal:
"Yakubu was definitely offside, he is a big lad and our keeper could not see the play.
"Howard Webb is a good referee and he was in no position to see it, but he should expect to get assistance from his linesman, who could surely see.
"It influenced the game. I just want fair decisions and that was not fair.
"It's a mixture of emotions, frustration and anger, because we had opportunities to score the first goal of the game.
"But if we continue playing and performing as well as that, we'll be fine.
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