It seemed the heroics of Forest goalkeeper Karl Darlow would help the Reds to a point after midfielder Djamel Abdoun was sent off in the 34th minute for conceding a penalty with a clumsy foul on Neal Bishop.
Darlow pushed away Tom Ince's penalty and looked to be on course for a clean sheet, before Dobbie popped up in the 91st minute to snatch a big win for Blackpool, over one of their promotion rivals.
The result extended Forest's stuttering run of form, which saw them follow up last weekend's defeat at Yeovil with another loss, meaning Davies' side have now won only two of their last eight games.
The two main talking points of the first half had been a penalty appeal for Forest that was not given - and one for Blackpool that was. But referee Michael Naylor seemed to have got both decisions right.
Darius Henderson, in fact, was perhaps lucky not to be booked for diving, after going down dramatically as Kirk Broadfoot attempted to deny him the chance to collect the loose ball, after Matt Gilks had blocked his shot.
But Forest's Algerian winger, Abdoun, was subsequently sent off for hauling back Bishop, after the former Notts County man had snatched the ball off his toes in the box, to race clear.
Forest owed a debt of thanks to keeper Darlow for making an outstanding save, diving low to his right, to push away Ince's subsequent spot kick.
The Forest number one had already produced a brilliant stop to prevent Dobbie from breaking the deadlock, with a low, driven shot from well worked free kick.
But it was 10-man Forest who came closest to taking the lead before the interval, with skipper Chris Cohen, making his 250th start for the Reds, hammering a powerful shot from the edge of the box, which looked to be bound for the bottom corner before Matt Gilks got down late to push away.
Ince was denied for a second time by Darlow after the break, with the keeper equal to a testing volley that had bounced awkwardly in front of him.
Blackpool were going all out for the win, bringing no fewer than three attacking players off the bench in the final stages, in the form of Nathan Tyson, Steven Davies and Michael Chopra.
But it was Dobbie who arrived to sweep the ball into the bottom corner of the net in the 91st minute to secure a big win for Blackpool over one of their promotion rivals.