Lansbury levelled the scores just after half-time, with Forest going in at the interval trailing to Andrew Crofts' header just after the half hour mark.
Two goals in three minutes put Forest in the driving seat, with Lansbury slotting home from the spot almost immediately after Darius Henderson had given them the lead before Nathaniel Chalobah was sent off in the 67th minute as Forest finished the match with 10 men.
Brighton went into the game having scored only four goals in their previous five matches and, in a lively start, former Newcastle winger Kazenga LuaLua provided an immediate threat for the Seagulls.
More top news
Philippa has Sunday's weather for the east
Philippa has Sunday's weather for the west
A dramatic final day in the Sky Bet Championship saw Bournemouth crowned champions, after Watford falter