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Gus Poyet believes Sunderland need a miracle to survive relegation from the Premier League.

Their weary fans won’t believe they even exist after a disastrous afternoon sent them deeper into the mire.

But try telling that to the jubilant Evertonians who stayed long after the final-whistle to celebrate a record seventh successive Premier League win and a place in the top four.

Ask those fans and they’ll tell you emphatically that miracles can happen.

The Blues have hold of the reins in the race for Champions League qualification after Wes Brown’s own goal sent them two points clear of Arsenal with five games to go.

Roberto Martinez has taken Everton to a highest ever points total in the Premier League era and on course to smash through the division’s glass ceiling in his first season.

The Blues were far from their vintage best in a scrappy game with rock-bottom Sunderland but nevertheless they ground out a vital win in the North East on Saturday.

Martinez played down the psychological significance of overtaking Arsenal with a win but Everton have cranked up the pressure on their rivals an extra notch.

The Blues battered and bruised Arsenal six days’ earlier with one of their most impressive performances of the season but this performance will have left the Gunners feeling sick.

Everton toiled in the second-half as Sunderland rolled up their sleeves and piled on the pressure.

But Martinez’s men still found a way as Gerard Deulofeu stormed past Marcos Alonso and delivered a cross that was put into his own net by Brown.

Did Everton deserve to win? Probably not. But they found a way and it will have come as another body blow to Arsene Wenger’s men.

Not playing well and still winning? The sign of a good team and Arsenal know it.

Martinez spoke recently about how Wenger’s sides have developed a “real understanding” of what it takes to win games in a frantic, pressurised run-in in the Premier League era.

The Catalan’s Everton are still in their infancy but with only a handful of games left and the Blues in a strong position, it appears they are learning fast.

The examination lasts until the end of the campaign but with the power of momentum building by the week, you would not bet against Everton right now.

Crystal Palace, who look to have all but secured their safety, are the next test when they visit Goodison on Wednesday night.

Tony Pulis’ side are sure to provide typically organised and stubborn opposition but every Everton player is oozing with confidence.

And when you are in such a vein of form, results like at Sunderland happen.

Everton were handed a sizeable slice of luck when Brown sliced the ball past Vito Mannone but maybe the Blues were due it after the Sunderland’s goalkeeper stopped everything in the reverse fixture on Boxing Day.

That was Everton’s only defeat at Fortress Goodison this season and though Palace, Manchester United and City are still to come to Merseyside, Martinez will have few doubts that they can keep that run going.

The Blues also face trips to Southampton and Hull City in the final stretch and though, on paper at least, Arsenal’s fixtures look more favourable the Gunners appear incredibly fragile at present.

The same cannot be said of Everton who showed “concentration, grit and character”, to borrow the manager’s words, in keeping a determined Black Cats at bay.

John Stones, excellent again, twice made telling contributions.

First when clearing Fabio Borini’s effort off the line and then bravely sliding in when Tim Howard had fumbled a shot during a period of mayhem in the Everton area.

And James McCarthy – who else – ran harder, faster and for longer than anyone to block Adam Johnson’s goalbound shot in the first half when Sunderland had opened up the Blues.

It was a rare period of success for the home in an opening 45 minutes that Everton dominated.

Steven Naismith was guilty of an uncharacteristic rush of blood to the head when, after spinning inside Brown, he blazed his shot over the bar from eight yards.

Everton’s failure to convert their dominance only served to give Sunderland hope for the second-half and the troubled Wearsiders emerged with the bit between their teeth.

Stones’ lunge to clear the danger came in a period when Poyet’s men were at their best in the game but the experience of Sylvain Distin and Gareth Barry were pivotal in stabilising the side.

Indeed, there was a personal triumph for Barry at the Stadium of Light as the on-loan midfielder made it through the game without picking up the 10th booking of his season before yesterday’s yellow card amnesty.

Losing Barry for games with Palace and United – not to mention his ineligibility for the City fixture – would have been a disaster for Everton.

The gods are smiling down on Everton at present, it seems, although there’s only one man performing miracles at Goodison Park.