Liverpool produced a dominant first half display before allowing Bournemouth to overcome a two goal deficit and win the game with 3 goals in the final 15 minutes.
At times in the first half the home side struggled to get out of their own half, but they came back in the second half to expose Liverpool's defensive failings.
Joel Matip missed out with an ankle injury meaning a rare Premier League start for Lucas Leiva in central defence alongside Dejan Lovren.
Adam Lallana returned to the squad - named on the bench.
It was a sunny day on the South Coast and most of Liverpool's football in the opening period was just as bright.
The reds dominated from the outset but patiently waited until the 20th minute when Sadio Mane broke the deadlock. He latched on to a forward pass from Emre Can and poked it past the keeper.
Seconds after the restart and Divock Origi scored a sensational goal as his angle to goal narrowed and the reds looked comfortable most of the way until half time.
Bournemouth did have a first half penalty shout but the referee waved it away. It initially looked a strong appeal by the hosts but on repeated viewing looked less and less like a spot kick.
Second half implosion
Second half was a different story. Bournemouth looked determined - Liverpool looked like they were going through the motions.
The reds did give away a penalty in this half - and it came from a clumsy challenge from James Milner. Callum Wilson stepped up to open the scoring for Bournemouth.
But just as the reds faced pressure - Emre Can collected a pass from Sadio Mane and fired in a curler to restore the two goal advantage. 3-1.
All over? Not quite - the reds were about to implode
From a Liverpool attack the ball ended up pinging across Liverpool's penalty area. It bounced off Afobe's heels and Ryan Fraser smashed it in.
Two minutes later Bournemouth were level.
A cross from Fraser and centre-back Cook span and volleyed the ball into the net. As the time ticked on it was the Cherry's who looked most likely to win.
And so they did.
In the third minute of stoppage time Karius spilled a shot from Cook and Nathan Ake made it 4-3 as Liverpool lost their first game in 15.
Liverpool stay in 3rd place in the Premier League but there is now a 4 point gap to the leaders Chelsea.