Burnley's brave bid to improve their frustrating away record came to nothing as two late goals ended the Clarets' resistance and saw Everton climb above them in a congested scrap to stay clear of the Barclays Premier League relegation zone.
Owen Coyle's men turned in a fighting performance in their bid to stop the rot away from Turf Moor.
And they could have won it had David Nugent's second half chance gone in rather than hit a post on his return to Merseyside.
But after Stephen Jordan was sent off for two bookable offences with just under half an hour to go - as Burnley's yellow card count harshly rose towards five - the Clarets were forced to defend.
They did so stoically but their back line was finally breached in the 83rd-minute when substitute James Vaughan forced the ball home at the far post with Yakubu getting away with standing in an off-side position.
Yakubu, partially obscured by Jensen, is offside as Vaughan opens the scoring
And after the Clarets had thrown men forward and done their best to force a late leveller they were caught out in stoppage time when Stephen Pienaar drove home Everton's second.
With Coyle naming the same side and formation that had come back to earn a point against Bolton 48 hours earlier it was clear that Burnley were prepared to be positive to try and end a memorable year with a first away success in the Barclays Premier League.
Fighting fire with fire was always likely to give the home side opportunities, though, and the Clarets had to weather something of an early storm.
Inside the first minute Yakubu got away and pulled the ball back for Leon Osman who should have done better.
And the Clarets then held their collective breath when a shot from Yakubu hit Michael Duff on the arm only for the defender to get the benefit of the doubt from referee Howard Webb.
However, Everton, without a home win since September, failed to make the most of a number of promising positions and the Clarets countered with Steven Fletcher forcing Tim Howard into a decent save after showing typically precise control to take down a Jordan pass and work the opening.
When Burnley attacked in numbers and moved the ball around swiftly they carried a threat and another patient move ended with Wade Elliott, who had scored the winner when the teams met in August, seeing a low shot turned past the post by Howard.
From the resulting corner, Duff headed down and Andre Bikey was unlucky to see his fiercely struck volley hit Tim Cahill on the six-yard line.
But, despite a half-chance for Nugent from Lucas Neill's weak back header, much of the pressure continued to come from Everton and with 23 minutes gone they hit the post. Again Yakubu got free but from Leighton Baines' ball forward he could not quite steer his side-footed volley on target.
And ten minutes later the Toffees went close again when Diniyar Bilyaletdinov got past Jordan but could not beat Brian Jensen, who got down quickly to save well to his right-hand side.
But the Clarets had gained a foothold in the game and they started the second half in encouraging style, closing down more quickly and making the home side increasingly edgy.
Chris Eagles launched a couple of his trademark runs and from one covered some 75 yards before leaving the ball for Kevin McDonald whose curling shot drifted wide.
And with 57 minutes gone only the width of the post prevented the Clarets from going ahead.
Nugent hits the post
Eagles won and delivered another corner which was half cleared only as far as Elliott. He poked the ball forward to Nugent and on the turn the striker, an Everton fan as a boy, just failed to score his dream goal in front of 25 members of his family as his effort bounced out off the far post.
That proved to be Nugent's final contribution as he was sacrificed when Burnley were reduced to ten men with 63 minutes gone.
Jordan, who was booked in the first half for a foul on Bilyaletdinov, needlessly pulled back Pienaar to become the first player in 100 league games between the two clubs to be dismissed, although for the full-back it was his second red card on this ground after a previous dismissal playing for Manchester City.
Coyle sent on Christian Kalvenes to get his back four up to strength but from one of the Norwegian's first touches his attempted clearance cannoned up into the air off Marouane Fellaini and allowed Yakubu the chance to direct a looping header towards the top corner before Jensen made a fine save at full stretch to palm the ball away.
And that prompted a magnificent rearguard action from the Clarets with Duff a tower of strength at the back as Coyle's men looked to hold on and claim a notable point.
They looked set to do it but with just seven minutes to go Burnley's resistance was ended. A low cross from Fellaini reached Vaughan at the far post via an unfortunate deflection off Kalvenes and the substitute scrambled the ball home past Yakubu, who appeared to be in an off-side position on the goalline.
Eagles and McDonald hit back with shots in the dying moments which forced Howard to save but Burnley could not force a leveller and in stoppage time Pienaar ran onto Yakubu's pass to bury a shot and again leave the Clarets heading home empty-handed.
Burnley: Jensen, Alexander, Duff, McDonald, Fletcher (Thompson 82), Elliott (Blake 85), Mears, Bikey, Nugent (Kalvenes 65), Jordan, Eagles. Subs: Penny, Gudjonsson, Edgar, Guerrero.
Everton: Hibbert, Baines, Heitinga, Bilyaletdinov (Vaughan 82), Cahill (Neville 58), Pienaar, Osman, Yakubu, Neill, Howard, Fellaini. Subs: Nash, Coleman, Duffy, Agard, Baxter.
Referee: Howard Webb.