Manager Billy Davies praised his players after a game which he still felt Forest would win even after they trailed to Andrew Crofts' goal for the Seagulls.
Henri Lansbury scored twice and Darius Henderson then provided the cushion which allowed the Reds to ride the sending off of Nathaniel Chalobah.
"This team never say die, never, and it was a great three points," said Davies afterwards.
"It wasn't one of our most emphatic wins but away from home we've done very well. The Brighton keeper made three or four great saves in the first half and we were disappointed to go in one nil down."