The Reds were cruising to victory after Emre Can had restored Liverpool's two-goal advantage midway through the second half after Callum Wilson's penalty got Bournemouth off the mark.
But the away side fell apart under persistent pressure from Eddie Howe's men, with substitute Ryan Fraser proving influential.
Fraser fired into the bottom corner before Steve Cook showed great footwork to fire the home side level before Ake bundled the ball after a howler from Loris Karius in the Liverpool goal.
It had been all too easy for Liverpool in the first-half after they established a two-goal lead going into half-time.
Sadio Mane was sent clear by Emre Can before prodding the ball beyond Artur Boruc, before Divock Origi took the ball round the stranded goalkeeper from outside the area before finding the bottom corner with a stunning clipped finish.
More pictures after the cut...
Total scoreline at the premier weekend:
Bournemouth 4 vs Liverpool 3
Man. City 1 vs Chelsea 3
Sunderland 2 vs Leicester City 1
Tottenham 5 vs Swansea City0
Crystal Palace 3 vs Southampton 0
Stoke City 2 vs Burnley FC 0
West Brom 3 vs Watford 1
West Ham 1 vs Arsenal 5
Everton 1 vs Man United 1
Meanwhile; Middlesbrough vs Hull City are yet to play on Monday, 5 December at 8:00 PM.
