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.
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.
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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