Brentford goalkeeper David Raya punched away a cross from the right and Forest's Morgan Gibbs-White had his effort blocked before the ball ricocheted off Jorgensen and over the line, with the goal given after a VAR check for offside.
Despite earning a crucial point, Forest remain rooted to the bottom of the table on 10 points from 14 games while Brentford move up to 10th with 16 points.
"We got that equaliser right at the end which I felt was fully deserved but we should have got three points," Gibbs-White said. "I'm just happy we didn't come away with no points."
The hosts deservedly took the lead in the 20th minute when Gibbs-White squeezed past three Brentford defenders and curled home from the edge of the box for his first Forest goal.
Brentford were awarded a spot-kick following a lengthy VAR check in the closing minutes of the first half when Yoanne Wissa went down after taking the ball around goalkeeper Dean Henderson, with Bryan Mbeumo coolly converting to level the score.
The visitors went ahead with 15 minutes remaining when Mathias Jensen lofted a through ball to Wissa and the forward lobbed Henderson with a cool finish, before Forest escaped with a point in the dying seconds.
"Of course that's tough to take when you're leading in extra time," Brentford boss Thomas Frank said. "I'm proud of the team.
"The way we played the second half made me very proud but when you lead 2-1 in extra time you have to win."