Brentford took their lead at the top of League Two to four points, but the win was soured by the dismissal of Darren Powell for fighting with a team-mate.
Billy Clarke gave the Bees the lead when he got his head to Sam Wood's shot to guide it past Shwan Jalal.
But the Bees were reduced to 10 men when Powell was shown a straight red for a scuffle with Karleigh Osborne.
Bournemouth rallied and Anton Robinson shot over, but they were frustrated and now sit just a point off the drop zone.
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