Billy Clarke's goal four minutes before half-time proved to be Brentford's winner after they had played almost the entire second half with only ten men.
Evergreen defender Darren Powell was sent off after an altercation with one of his own team-mates.
The 35-year-old was red-carded by referee Gavin Ward two minutes into the second half after appearing to shove fellow defender Karleigh Osborne in the chest.
The pair were involved in an angry verbal exchange as Brentford repelled heavy Bournemouth pressure at the start of the second half. According to manager Andy Scott, the pair patched up their differences in the dressing room after Brentford's 1-0 win.
Brentford, who had drawn their previous three matches, were well worth their first League Two success since beating Barnet on March 10.
Their victory owed much to the predatory skills of on-loan Clarke, whose unselfish, non-stop work-rate was a key factor in Brentford's success.
Clarke worked tirelessly for the divisional leaders, fetching and carrying in a deep lying role. But his goal four minutes before half-time did have an element of luck about it.
Sam Wood fired a speculative shot from 20 yards, but Clarke got in a crucial touch - his glancing header diverting the ball into the top right-hand corner of the Bournemouth goal.
It was about the last effort on goal that Brentford had in the match, Bournemouth enjoying considerable pressure thereafter, but despite their numerical superiority, seldom looked like penetrating Brentford's resolute defence.
After a frenetic early second-half period, in which Powell was sent off, Bournemouth huffed and puffed but seldom looked like breaking the Brentford defence down.
Bournemouth's defeat was their second of the Easter weekend - they lost 1-0 at Barnet on Saturday - and has left the financially crippled south coast club in deep relegation trouble, just one point above the danger-zone, with three matches left to play.
Significantly, Bournemouth's next two matches are against Chester City and Grimsby Town, the two other clubs deep in relegation trouble.
But Bournemouth have only managed one win in their last five matches and are sliding deeper into the mire.