The Bees were under pressure for long periods, but a solid display from goalkeeper David Button helped to preserve their clean sheet.
Oldham created the better first-half chances, with Jonson Clarke-Harris twice heading off target before he was denied by Button's quick reactions.
Danny Philliskirk also headed over from just three yards for the Latics, claiming he was shoved in the back as he met a cross from Gary Harkins.
Brentford posed their first real threat moments before the break when Clayton Donaldson forced a good save from home goalkeeper Paul Rachubka.
But Button rescued Brentford again, keeping out James Wilson in the 48th minute, before Harkins went close with a mazy run and shot.
Oldham substitute James Dayton wasted a clear opportunity as the home side continued to test the dogged Bees defence.
Brentford's best chance arrived six minutes from time, but Stuart Dallas was unable to beat Rachubka at his near post.