They avoided equalling an unenviable club record of nine successive home games without a win and, while only their third triumph in 18 games, it extends their unbeaten Premier League run to five games.

And having opened up a gap to the relegation zone, Moyes’s men can go into the New Year looking up the table rather than over their shoulders.

Everton’s one change from the team that eventually prised a point from the Stadium of Light on Boxing Day was an enforced one, with Louis Saha missing out with a hamstring problem – surprisingly only his second absence from a league game this season.

It gave Yakubu the chance from the start to realise his ambition of signing off his Premier League efforts with a goal before departing for the African Cup of Nations with Nigeria next month.

The striker came close in the 22nd minute when failing to properly control a fine cross from the left by Leighton Baines, the ball looping away from Burnley keeper Jensen and smacking against the post.

It summed up Everton’s endeavours during an entertaining if frustrating first half in which, as at Sunderland before Marouane Fellaini found a late way through, they created chances but failed to find the finish to match.

The signs were there from the first minute, when Pienaar released Yakubu down the right but Leon Osman couldn’t control the Nigerian’s cutback before the Burnley defence ushered the ball clear.

There was fury on the pitch and in the stands in the fifth minute when referee Howard Webb chose to ignore Everton’s claims for a penalty despite Yakubu’s shot clearly striking the left hand of centre-back Michael Duff.

Osman, again employed in a central position, then twice had openings but struck the first at Jensen and then rushed a shot wide.

The Burnley keeper was required to make a much more impressive save in the 33rd minute, when Diniyar Bilyaletdinov barged his way past left-back Jordan on to Pienaar’s pass but directed his side-footed shot too close to Jensen, who parried clear low down to his right.

Burnley, though, weren’t without their openings, and were almost rewarded for manager Coyle’s persistence in playing the passing game with a purple patch midway through the half.

After Steven Fletcher’s snapshot from 20 yards solicited a smart parry by Tim Howard, the Everton goalkeeper was required to make a similar stop to deny Wade Elliott. From the resultant corner, Andre Bikey’s goalbound volley was well blocked by a brave Cahill.

Both defences appeared teetering on the brink throughout, and Burnley almost capitalised on slackness in the Everton backline shortly after the interval.

A direct run from Chris Eagles down the left ended with Kevin McDonald slicing a shot that flew across the face of goal, before a failure to clear a Burnley corner gave Elliott the chance to feed the ball into the back of the box where Nugent, an Everton fan who attended the FA Cup final in May, shot against the same post Yakubu had in the first half.

Yet the dynamic of the game turned again when the hapless Jordan, earlier cautioned for fouling Bilyaletdinov, picked up a second yellow card for a silly tug on Pienaar’s shirt.

Fellaini glanced a Baines cross at Jensen and the goalkeeper stretched to palm over a Yakubu header after substitute Christian Kalvenes’s clearance ricocheted fortuitously off the Nigerian.

The handball penalty shouts were balanced out in the 69th minute when Webb ignored Burnley claims after Graham Alexander’s cross struck a sliding Lucas Neill on the arm.

But Everton had finally wrested an initiative they were never to relinquish. A shot from Baines was deflected behind after a clever combination with Pienaar, Bilyaletdinov had a speculative effort blocked and Pienaar slashed wide.

The goal had to come, and it arrived six minutes from time. After Fellaini and Pienaar exchanged passes down the left, the latter’s low cross was missed by Yakubu and rolled into the path of Vaughan to sidefoot home.

Yakubu then helped make the game safe in injury time, winning the ball off a tired Alexander before advancing and slipping in Pienaar, who thundered a left-foot finish beyond Jensen and ensure a happy New Year for Everton.