The game was soured by the dismissal of Darren Powell for fighting with team-mate Karleigh Osborne.
Billy Clarke had given the Bees the lead four minutes before half-time in somewhat fortunate fashion when he diverted Sam Wood's shot past Shwan Jalal.
However the Bees were reduced to 10 men four minutes after the break when Powell was shown a straight red for a scuffle with Osborne, who received a booking.
Bournemouth tried to make the numerical advantage count and Anton Robinson shot over the bar from the edge of the box.
Danny Hollands also dragged a shot wide after finding space in the box as Brentford held on for a much-needed victory that kept Bournemouth in relegation trouble.