The Seagulls led at the break thanks to an Andrew Crofts goal midway through the half, but a double from Henri Lansbury coupled with a strike from Darius Henderson saw Billy Davies's men leave with all three points.
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Karl Darlow prevented Ashley Barnes from opening the scoring in the first half, but he could not stop Crofts from planting a header past him in the 31st minute.
It did not take long after the break for Forest to draw level, with Henri Lansbury scoring within a minute of the restart.
Darius Henderson put them ahead on the hour mark, before the former Arsenal man grabbed his second of the game two minutes later.
The result sees Forest finish the day in fourth place in the Championship.