The visitors were on terms within 60 seconds of the restart, midfielder Lansbury rising to level with a superb header from 8 yards following a corner from Majewski.
Keeper Darlow prevented** **Brighton from regaining the lead only 3 minutes later by pushing a goal-bound shot from Barnes onto the post.
Two goals in the space of two minutes put Forest firmly in charge with a strike from Henderson and a spot kick by Lansbury boosting the visitors.
Forest were reduced to 10 men on 67 minutes when Chalobah, booked earlier for a foul, received a second yellow for a push on LuaLua.
LuaLua had a curling free kick saved by Darlow as the Seagulls struggled to launch a late fightback.