Paul McShane's second-half header earned Brighton a first away win of the season and ended Crystal Palace's run of three successive victories.
A fiercely-contested match between the two bitter rivals was full of incident but short on quality.
The winner came in the 78th minute when McShane rose to head in Sebastien Carole's corner.
Brighton midfielder Richard Carpenter went off after 25 minutes after he was caught by a stray arm from Tom Soares.
Crystal Palace manager Iain Dowie:
"What was said in the dressing room stays there but yes, I'm disappointed and angry.
"That was not a performance I want to be associated with this football club.
"I'm not happy, and neither should the players be. We didn't put the extra 10% in that you need. Our options were limited, our movement wasn't there."
Brighton manager Mark McGhee:
"It was a close game, but we played well enough to win.
"We've played like that away from home this season, and we've drawn games we should have won and lost games we should have drawn.
"When we play at places like this, and with an atmosphere like this, it shows just what we're capable of."
Crystal Palace: Kiraly, Butterfield, Ward, Fitz Hall, Boyce, McAnuff (Andrews 83), Soares, Hughes, Reich (Watson 73), Freedman (Macken 63), Morrison.
Subs Not Used: Borrowdale, Speroni.
Brighton: Henderson, Carole, McShane, Butters, Reid, Carpenter (Frutos 25), Hammond, Oatway, Hart, Robinson (Kazim-Richards 71), Knight (El-Abd 90).
Subs Not Used: Mayo, Blayney.
Goals: McShane 79.
Ref: A Hall (W Midlands).