Free-scoring midfielder Scott Murray netted his 19th goal of the season as Second Division Bristol City booked their place in the Southern Section Final after a controversial clash on the South Coast.
Murray rounded off the scoring deep into injury time after defender Mickey Bell had struck twice as the visitors came from behind to notch their first victory in five games.
Bournemouth took the lead on 15 minutes when captain Carl Fletcher headed his first goal of the season to make it 1-0.
The home side were reduced to ten men on half when Marcus Browning picked up his second booking after a tussle with City defender Tony Butler.
It became ten against ten when centre-back Butler was dismissed 13 minutes into the second half after picked up his second yellow card of the game.