After a quiet start, the game’s opening chance came midway through the first half for Marcus Tavernier, who cut inside before curling just wide. Alex Scott then fired over from distance, before James Hill directed his header the same way from much closer range.
Ryan Christie also managed to round the returning Caoimhin Kelleher before running the ball out of play, but the best opportunity before half-time fell to Tavernier, who produced the only shot on target by working Kelleher from a tight angle.
Brentford were second-best, having offered just two attempts at goal themselves, and suffered a blow when Rico Henry was forced off injured in the 21st minute, replaced by Kristoffer Ajer.
There was not much in the way of goalmouth action at either end heading into the break, meaning both sides went into the break goalless, with Bournemouth 45 minutes from a league-high 13th draw of the season.
Tavernier came even closer to scoring immediately in the second half when he clipped the post after sliding in for a cross, and was perhaps unlucky not to get a penalty when Michael Kayode appeared to have halted his balance.
Brentford stayed in the game, though, and finally managed to conjure up their first shot on target in the 73rd minute, but it was a weak one as Dango Ouattara failed to get a clean contact on his effort to trouble Dorde Petrovic.
Bournemouth’s goalkeeper did have to make a better save shortly after, denying Sepp van den Berg the breakthrough.
Heading into the latter stages, Bournemouth remained threatening themselves, and Tavernier could not believe his luck when he struck the post again from a narrow angle.
Evanilson then thought he provided the magic needed to find a possible winner, but his goal was disallowed for offside after some neat footwork.
Despite a spirited performance, the Cherries could not find what would have been their first win in nine H2Hs against Brentford (D3, L6), as the Bees added another point to help push them further in their European charge, staying seventh in the table, four points above Bournemouth in ninth.
Flashscore Man of the Match: Marcus Tavernier (Bournemouth)