George Thorne, with a thunderous long-range strike in the 76th minute, and Jeff Hendrick added further goals before Kazenga Lualua fired in an 89th-minute consolation for Brighton.
Derby, led by former England manager Steve McClaren, will face Wigan Athletic or Queens Park Rangers on May 24 for a place in the Premier League.
(Reporting by Tom Hayward, editing by Ed Osmond)
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