The Bees took an early lead as Jonathan Douglas celebrated signing a new contract by firing home after Alex Pritchard's cross.
However, Marc Pugh levelled the scores soon after following a defensive mix-up.
But, just before half-time, Brentford retook the lead as Pritchard's free-kick squirmed past Artur Boruc on the Cherries' goal.
Bournemouth piled forward in the second half looking for an equaliser and Jota hit the bar on the counter-attack.
And Brentford secured the points as Chris Long scored his first goal for the club, turning home Pritchard's cross.