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Gary Hart was the hero for the South Coast club with an 81st minute winner after Paul Reid's early opener had been cancelled out by a controversial Robbie Blake penalty for Leeds.
The Yorkshiremen started full of confidence following four straight wins and could have gone ahead in the third minute, captain Paul Butler heading wide from Blake's quickly taken free-kick.
Brighton stunned the visitors by going ahead in the 10th minute. Reid, recalled on the right side of midfield, nipped in unmarked at the near post to meet a low cross from Alex Frutos with the outside of his right foot.
Dean Hammond headed against the post from a corner for Brighton and stabbed just wide either side of Reid's goal before Leeds were handed a hotly disputed route back into the game.
Demoted Premiership ref Andy D'Urso awarded a spot-kick in the 38th minute against Reid for an innocuous looking incident involving Eddie Lewis.
Brighton's Australian goalscorer was trying to shield a cross away from the American midfielder but D'Urso decided it was a penalty and Blake converted via a post.
Blake had earlier been denied when his volley was headed off the line by Brighton full-back Adam El-Abd in a lively first half.
Chances were few and far between for both teams after the break, but it was Hart who popped up with nine minutes left to earn Brighton their fifth win of the campaign.
The versatile stalwart, playing up front in a new partnership with Sebastien Carole, met Reid's cross at the near post with a first-time shot into the roof of the net.
Richard Cresswell headed onto the roof of the Brighton net twice in the closing stages, but a late Leeds flurry was not enough to preserve their unbeaten run.