Bobby Zamora's quickly taken free kick caught the Forest defence unawares as former Fulham winger Brooker slotted his fifth of the campaign past Darren Ward. It was no more than Brighton deserved in a first half which they dominated.
Midfielder Richard Carpenter had a long-range shot parried by the diving Ward and then crashed another effort from outside the box against the crossbar.
All Forest could offer by way of response in the opening 45 minutes was a 20-yard drive by French full back Matthieu Louis Jean, which former Forest veteran Dave Beasant turned away for a corner.
The decision by Forest boss Paul Hart to employ a three man attack comprising fit-again top scorer David Johnson, Marlon Harewood and Darren Huckerby backfired as they slumped to their first league defeat in ten games.
The 24-goal Johnson, making his first start since recovering from knee surgery, had two penalty claims in the second half.
Referee Richard Beeby rejected the first when Brighton captain Danny Cullip appeared to bundle him over.
Beeby awarded a spot kick when Johnson went down inside the area again, but then he noticed his linesman flagging that the Forest marksman was offside and awarded Brighton a free kick instead.
Andy Reid almost snatched an equaliser for the visitors when he cracked a 25-yarder against the bar with nine minutes left.
Brighton boss Steve Coppell said: "We worked hard for this. It wasn't just dumped in our lap.
We prepared hard for the game, because Forest are a quality side.
They hadn't been beaten since December in the league, which shows what they are all about.
"Our performance had a little bit of everything. We created some good opportunities and dug in when we had to."
Hart admitted: "Brighton deserved to win. We were ordinary all over the park."