Liverpool took the lead through winger Sadio Mane in the 20th minute, before forward Divock Origi doubled their lead just two minutes later.
With the Merseysiders in the driving seat, Bournemouth struck back through a Callum Wilson penalty in the 56th minute.
Emre Can added a third for Liverpool a few minutes later, but goals from Ryan Fraser and Steve Cook restored parity in the game.
Nathan Ake then scored deep into stoppage time to hand Bournemouth a dramatic 4-3 win. Despite the loss, Liverpool stay third in the league standings.