The Bees, unbeaten in 11, and the Cherries, without a defeat in 15, created few chances in a game of cat and mouse.
Brentford were denied an injury-time penalty when striker Clayton Donaldson was bundled over by Bournemouth defender Tommy Elphick.
Referee Tim Robinson waved play on, sparking furious scenes on the touchline as Brentford boss Uwe Rosler remonstrated with the fourth official.
Brentford's on-loan striker Marcello Trotta came closest to breaking the deadlock for the hosts in the first half, forcing Bournemouth goalkeeper David James into a reflex save from his fierce angled drive.
Adam Forshaw also drifted an effort just wide for the Londoners, while Marc Pugh's drive was punched clear by Brentford goalkeeper Simon Moore.
The game opened up after the break and Wes Fogden thought he had given the Cherries the lead, only to see his low drive blocked by Jake Bidwell.
Seconds later Brett Pitman's effort from eight yards was cleared off the goalline by Bees centre-back Harlee Dean.
It was end-to-end stuff as the game opened up towards the end, with Bournemouth substitute Josh McQuoid slicing wide when well placed.