Yoane Wissa thought that he had won it for the visitors in the 75th minute of the contest, with Bryan Mbuemo levelling the scores for Thomas Frank's side after Morgan Gibbs-White had made the breakthrough.
However, Forest secured a point in the final moments, with Mathias Jorgensen's own goal in the 96th minute ensuring that the spoils would be shared at the conclusion of a pulsating contest.
Steve Cooper's side remain bottom of the Premier League table despite the late point, while Brentford sit 10th, boasting 16 points from their 14 league games this term.
Wissa had the first half-chance of the match in the 10th minute, but the forward headed over the Forest crossbar from inside the penalty box.
Forest had a penalty shout in the 13th minute when Emmanuel Dennis raced into the penalty box and was tripped by Mathias Jensen, but the referee was happy for the play to continue.
Brennan Johnson saw his effort kept out by Brentford goalkeeper David Raya in the 15th minute, but the Reds were threatening, and they made the breakthrough in the 20th minute through Morgan Gibbs-White.
It was a brilliant effort from the summer arrival, who worked his way into a dangerous area before picking out the back of the net with powerful strike, which took a slight deflection.
Brentford were level late in the first half, though, with Mbuemo scoring from the penalty spot after Wissa had been brought down by Forest goalkeeper Dean Henderson, with the decision made after the referee was sent across to the monitor at the side of the pitch following advice from VAR.
The Bees then took the lead in the 75th minute when Wissa expertly clipped the ball over the onrushing Henderson after breaking into a one-on-one situation.
However, there was to be late drama at the City Ground, with Jorgensen being credited with the own goal after Ben Mee had cleared a Gibbs-White effort off the line.