Millwall was deservedly ahead at the interval thanks to Shaun Williams's header from a corner in the 15th minute, but its superiority did not last.
Lewis Grabban made a stunning impact from the Forest bench when he scored with his first touch 55 seconds after coming on, nodding in from close range.
He then appeared to have won the game for Forest by tapping in from Sammy Ameobi's ball in the 88th minute.
But O'Brien rescued a point for the Lions near the end, the Republic Of Ireland international turning home after Brice Samba could only palm Williams's long-range effort into his path.
Forest remains fourth on the table but could be overtaken by several teams over the weekend. Millwall has moved up to 11th.