Bournemouth 2 Everton 1: Ryan Fraser double takes Eddie Howe's side out of the relegation zone

Sometimes, all it takes is a moment of fortune. Having battled away fruitlessly for so long, and wasted a whole series of rare chances against a surprisingly charitable Sam Allardyce side, Bournemouth looked destined to leave the Vitality Stadium having extended their winless run in the Premier League to a record nine games.

But then a low shot from Ryan Fraser squirmed off an Everton foot and bobbled softly into the back of Jordan Pickford’s net. Just like that, Bournemouth brought this sorry run of form to an end and soared out the relegation zone in time for New Year.

“It would have been really, really hard on us not to win today,” said manager Eddie Howe. “The players showed they can dig really deep when they need to again.”

The three points were the least his side deserved from a performance in which they created enough opportunities to defeat Everton four times over and were only held back by their own defensive frailties. The visitors could force just the one shot on target, and Sam Allardyce can have few complaints about his first defeat as Everton manager.

“Some of the players were quite nervous in possession and I don’t know why,” said Allardyce, who could be thankful to goalkeeper Pickford that the defeat was not more emphatic.

“He is top drawer goalkeeper and a top lad,” said Allardyce. “I knew he would be a top goalie but I didn’t think it would be this quick. The players should be disappointed they have let him down today.”

Jordon Ibe, Callum Wilson and Benik Afobe could all have found the net for Bournemouth long before Fraser’s added to his fine first-half volley with his late deflected effort.

Also in Fraser’s debt is defender Steve Cook, whose error had allowed Everton’s Idrissa Gueye to fire home an undeserved equaliser shortly after half-time.

These details, one suspects, will be forgotten soon enough. Such was the relief at the Vitality at full-time, and the width of the smile of Howe’s smile at the final whistle, that it seems they have been cleared from the memory already.

“Today had been very easy,” Howe said. “We dominated the game and looked comfortable. To suddenly give them a goal could have easily changed the momentum of the match, given the run we have been on. That’s the truly impressive thing about the performance.”

His side had taken the lead after little more than half an hour. James McCarthy, making his first league appearance for Everton this season, passed straight to Wilson, who found the overlapping Josh King on the right. King’s cross picked out the busy Fraser at the back post, where he contorted his body acrobatically to fire past Pickford.

After the break, Cook’s error allowed Everton substitute Oumar Niasse to tee up Gueye for the equaliser, prompting the Bournemouth onslaught. Afobe, twice, Wilson again and Simon Francis all had chances, while Ibe struck the bar with a powerful drive before Bournemouth’s luck finally turned with just two minutes to spare.