After the weekend defeat to Wolves, Forest did not want to waste the chance to keep pace with the leaders and they moved into third with the three points.
Paul Hart's side appeared to be cruising to victory when they surged into a three-goal advantage but Brighton battled back in the last ten minutes to leave the hosts begging for the final whistle.
Marlon Harewood fired Forest ahead after eight minutes and the prolific David Johnson doubled the lead on the stroke of half-time.
When Jack Lester headed Forest further in front with less than 15 minutes remaining, it seemed to be game, set and match to the home side.
But Steven Sidwell handed Brighton a lifeline with ten minutes left on the clock and Nathan Jones's injury-time strike teed up a tense finish but Forest clung onto the points.
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