The Bees were in the ascendancy from the moment DJ Campbell equalised an early opener from Kris Commons.
And when Forest had Julian Bennett sent off after only 36 minutes for two bookable offences, they looked set for defeat.
But a combination of terrible misses from Lloyd Owusu and Kevin O'Connor, a goalline block from Wes Morgan and fine saves from Paul Gerrard earned the visitors an unlikely point.
Forest went ahead after only five minutes when Bees keeper Ademola Bankole, chosen for the first time ahead of Stuart Nelson, inexplicably came two yards out of his box to punch the ball.
Commons took the free-kick and saw it deflect into the net to break the deadlock.
In a tumultuous game, Brentford fought back and equalised when Campbell hit the bar and then side-footed home following a six-yard box melee in the 34th minute.
Forest's problems were deepened a minute later when defender Bennett, who had already been booked, cynically brought down Campbell after being out-thought on the wing. He was duly sent off and the home side grew in confidence.
Keeper Gerrard turned a Ricky Newman 20-yarder round the post after that and denied the same player when Owusu put the midfielder through just before half-time.
The second half was all Brentford but somehow the ball stayed out of the net as the Bees piled forward.
O'Connor missed a glorious chance by firing high from 10 yards, while Campbell also went close and Owusu somehow drove wide after turning his man.
Forest had a couple of chances themselves from free-kicks but were barely in the game and were relieved when Gerrard turned a Paul Brooker shot around the post and Morgan blocked Campbell's volley on the line.