In an open first half, both sides had chances to score, with Lee Camp needing to be alert to keep out Moses Odubajo and Jonathan Douglas.
Both sides continued in the same vein during the second half as opportunities to score came and went, with Kermorgant and Callum Wilson going close for the Cherries, while Alan Judge and Tony Craig were denied for the Bees.
In the end, it fell to Stanislas to give Bournemouth the lead from close range after a pinpoint Ryan Fraser cross.
Brentford refused to give up and were nearly rewarded for their persistence when Alan McCormack's cross reached Nick Proschwitz, only for his header crash against the bar in the dying seconds.
Bournemouth were able to hold on and now have six points from a possible six, while the Bees are still in search of a first league victory this season.