Ryan Fraser may want to claim a double for the Cherries but his 89th minute shot was definitely going wide.

At least it was until it struck the foot of unlucky England defender Keane – and in doing so took a wicked deflection past helpless Toffees keeper Jordan Pickford.

To be fair to Scottish midfielder Fraser, who had opened the scoring in the first half, he did not seem to care a jot as he ran off celebrating in front of a delirious Vitality Stadium.

For no matter how it actually went in, the effort finally ended Bournemouth’s worst winless streak at Premier League level.

And you only needed to look at the table afterwards to see how vital this first victory in nine was for Howe’s men.

The three points lifted them out of the bottom three to the giddy heights of 14th in the table – a jump of four places to ease their relegation worries for now.

New Everton boss Allardyce could scarcely believe he had tasted defeat for the first time in eight outings

Yet despite his side’s vastly improved second-half display – inspired by the half-time arrival of fit-again Wayne Rooney – Big Sam could have few complaints.

Until Roo’s entrance, and a rare goal from Idrissa Gueye, the Merseysiders had been dreadful.

This was not the result Everton wanted as they prepare to face Manchester United on New Year’s Day and then bitter-rivals Liverpool in the FA Cup on Friday.

Bournemouth’s 3-3 Boxing Day thriller here against West Ham had certainly suggested they were beginning to rediscover the attacking flair and form of their first two seasons at this level.

Yet, that mad game also rubberstamped their worrying fragility at the back. It made it 11 goals conceded in three games.

Little wonder with those sort of defensive stats they kicked off stuck inside the drop zone.

How Howe must have envied the rock-solid rearguard Allardyce had created in less than a month at Everton.

During that period his side had leaked only two goals – and in doing so had wiped away all worries of relegation, racing into the top half.

Not that their strikers had been exactly prolific of late. The Toffees arrived for their final clash of 2017 without a goal in 180 minutes.

All of which meant something was going to give - one way or another - on the south coast yesterday.

And in the early stages it sure looked more likely it would be Everton’s defence cracking as the Cherries began in lively fashion.

Jordan Ibe had already tested Pickford with a low drive when the home side’s greater tenacity and ambition was rewarded in the 33rd minute.

Everton midfielder James McCarthy, in his first start since October, gave away possession needlessly – and that error was punished in ruthless fashion.

Callum Wilson fed Josh King in down the right and he crossed for a completely unmarked Fraser to hook in a first-time, right-foot volley.

If that was a huge boost for the Cherries, the loss of Norwegian dangerman King to injury soon after was a potentially far more serious setback.

Without King’s pace, trickery and eye for goal, Howe’s side are not the same creative force.

Having produced a miserable one effort in 45 minutes – an off-target header from Dominic Calvert-Lewin - it was inevitable Rooney would come off the bench at the interval.

The England striker, who replaced McCarthy, had been in great scoring form before being struck down by a virus.

And just having him on the pitch inspired an immediate improvement in display.

That said it was Everton’s second sub of the day, Oumar Niasse, who was a integral to them drawing level in the 57th minute.

Along with Cherries defender Steve Cook - as he lost possession and then could only watch Niasse control a low cross and flick a beautiful lay-off into the path of Gueye.

Not renowned for scoring, the Everton ace made no mistake, calmly burying his shot past exposed Asmir Begovic.  It was his first league goal since February.

Howe and his side were kicking themselves at that stage, knowing they were in danger of wasting a brilliant opportunity to end the year on a high.

Credit to them, then, that refused to let heads drop or settle for a point.

That excellent attitude reaped dividends in the dying seconds with their best player Fraser deservedly being heavily involved in the killer winner at the death.