They always looked the better side, but home keeper Dimi Konstantopoulos made some great saves, and Hartlepool shook the Bees with a powerful second-half fightback.
But with 78 minutes on the clock Dudley Campbell, Brentford's best player on the day, sent Lloyd Owusu away for the winner, as Hartlepool appealed for a foul on Mark Tinkler.
Referee Uriah Rennie waved play on and the goal stood despite protests from the home team.
Campbell had given the Bees the lead on 22 minutes, when his neat header from a cross by Darren Pratley gave Konstantopoulos no chance.
The big Greek foiled Campbell soon after that with a brilliant one-handed save, and minutes later Eifion Williams blasted a good chance high over the bar as the home team threatened to equalise.
Konstantopoulos again saved from Campbell early in the second half, stopping a shot at his feet when a goal seemed certain.
On 72 minutes Pools drew level with a goal out of the blue.
The visiting defence failed to clear a corner and when Thomas Butler's shot came in, midfield man Tony Sweeney got the slightest touch on it to send his header into the roof of the net.
Then came Owusu's late winner, and Brentford deservedly hung on for the points.