NATHAN Ake struck a sensational stoppage-time winner as Cherries recovered from 3-1 down to beat title hopefuls Liverpool for the first time and record perhaps the finest victory in the club's history.

The home team appeared buried when Emre Can put the Reds 3-1 ahead in the second half, shortly after Callum Wilson's penalty had halved the deficit.

But substitute Ryan Fraser struck to keep the hosts alive, before Steve Cook squared matters. Sadio Mane and Divock Origi had scored to hand Liverpool a 2-0 interval lead.

Liverpool came into this game having run more than 1,500km this season, outstripping the distance covered by any of their Premier League counterparts.

And they started as if intent on doubling that total in one afternoon, with Cherries struggling to cope in the face of the Reds' cocktail of high pressing and crisp, quick passing.

The Reds' first chance, however, didn't arrive until 10 minutes in. Nathaniel Clyne scurried down the right on to Jordan Henderson's pass and crossed for Origi.

The Belgian striker was off-balance when the ball arrived in the middle, but he should have done far better than screw his effort wide of the far post.

Roberto Firmino had a thudding close-range effort blocked but there was no way out for Cherries.

Nevertheless, the crazy three-minute spell midway through the first half which saw Liverpool streak into a two-goal lead really could have been prevented.

Mane bundled his way in front of Ake to stride on to Can's lofted pass, struck from halfway. Artur Boruc hesitated, fatally, making the forward's mind up for him, Mane prodding beyond the keeper and into the net.

Still reeling from that 20th-minute blow, Harry Arter, so often the man hounding opponents out of possession, was dealt a taste of his own medicine.

It was Mane, three minutes after scoring, who proved too strong for the Cherries midfielder and helped the ball down the right for Henderson.

The Reds skipper, in turn, went forward to Origi, who must have been startled to look up and see Boruc bearing down on him.

Relocating the composure he had mislaid when presented with his previous chance, Origi rounded Cherries' number one and produced an emphatic finish, smashing the ball from an acute angle, unerringly into the far corner of goal.

When Cherries were finally able to muster some sort of response they found themselves – for a third consecutive week – deprived of any help from the officials.

Liverpool keeper Loris Karius made a meal of turning behind a Joshua King strike, with Junior Stanislas delivering the resultant corner from the right.

Wilson flicked the ball on for Ake, who took a tumble over Firmino's carelessly dangling leg. Referee Bobby Madley plainly felt Ake had gone looking for contact and ignored some pretty vehement penalty appeals.

Events seemed to be further conspiring against Cherries after the break, when Stanislas's afternoon was ended prematurely after he rolled his ankle under a tackle from Henderson.

Stanislas's replacement, Fraser, however, instantly made his mark.

Wilson seized on Dejan Lovren's weak header to knock the ball inside for the substitute. Left-back James Milner tried to tackle Fraser from the wrong side and only succeeded in tripping the Scot.

For the second week in a row, Wilson despatched his penalty into the bottom left corner of goal. Howe reshuffled his back four, brought Jordon Ibe – on at half-time for the ineffective King – across to the left and asked Fraser to raid down the right.

But before the changes could take effect, Liverpool had restored their two-goal advantage.

Mane beat Ibe to a loose ball and embarked on a jinking run into Cherries' box. The Senegalese's cut-back invited the advancing Can to shoot.

That he did, spectacularly rifling first-time, high to Boruc's left. If the keeper was at fault for the Reds' opening two goals, he was blameless here.

Boruc's next involvement saw him come perilously close to carrying Milner's left-wing corner over the line.

Between times Fraser shot straight down Karius's throat, the unconvincing German stopper just managing to paw the ball over his bar.

But there was no stopping Fraser with 15 minutes to play. Jack Wilshere and Arter swapped passes deep in their own territory, before the former – operating further back after Benik Afobe replaced Dan Gosling – found Afobe.

Fraser took over and fed Wilson, who crossed from the right. Afobe could not make contact. But Fraser could, gathering possession and firing inside Karius's left-hand post.

The door had opened for a second time. And, this time, Cherries walked through it.

Wilshere slipped a pass to Fraser on the right, after pouncing when Ibe's initial free-kick was only partially cleared.

The ubiquitous winger sent in a cross which was in Cook's general compass. The defender, his back to goal, took a sumptuous touch and spun in one movement. He then completed his star turn by stabbing the ball past Karius's outstretched right glove.

Afobe was then denied one on one by Karius, while Origi and Adam Lallana were narrowly off target as Liverpool tried to break the locals' hearts at the death.

But it was the Merseysiders who would suffer a late hammer blow.

Cook was given time to shoot from distance and duly obliged, sending in a bouncing effort that was too hot for Karius to handle.

Ake was first to the rebound, bundling past the keeper and knocking the ball home.

Cue bedlam.

MATCH STATS

Cherries: (4-4-1-1) Boruc; Francis, S Cook, Ake, A Smith; King (Ibe, h-t), Gosling (Afobe, 75), Arter, Stanislas (Fraser, 55); Wilshere; C Wilson.

Unused subs: Mings, B Smith, Pugh, Federici (g/k).

Booked: Wilshere, Francis.

Liverpool: (4-3-3) Karius; Clyne, Lovren, Lucas, Milner; Can, Henderson, Wijnaldum; Mane (Lallana, 69), Origi, Firmino.

Unused subs: Moreno, Klavan, Alexander-Arnold, Ejaria, Woodburn, Mignolet (g/k).

Booked: Henderson, Can.

Referee: Bobby Madley (West Yorkshire).