Bournemouth are finding Brentford a trickier task than Huddersfield Town, having been held by the Bees during the opening period at the Goldsands Stadium.
Brentford made a promising start when Moses Odubajo, a summer recruit from Leyton Orient, forced an early save out of Cherries keeper Lee Camp.
However, the hosts were equally threatening in the early exchanges as first Yann Kermorgant and then Tommy Elphick came close to giving Eddie Howe's side the lead.
Both teams had opportunities to score during a lively opening half-an-hour, with Jonathan Douglas seeing his header kept out midway through the half.
With the break approaching, Callum Wilson went close with a set-piece header, but failed to hit the target.
Bournemouth are looking to build on their 4-0 victory at Huddersfield Town last Saturday, while Brentford are searching for a first league win of the season, after drawing at home to Charlton Athletic.
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