In a cagey affair where Palace uncharacteristically owned the lion's share of possession, the visitors won with goals either side of a Luka Milivojevic penalty to claim six points in total from the claws of the Eagles.
Perhaps as an intense rivalry is expected to, the game started in fiery fashion when Anthony Knockaert saw yellow within a minute after an aggressive, lunging tackle on Palace captain Milivojevic.
Michy Batshuayi registered the afternoon's first shot on target as he dug-out an effort at Mat Ryan's goal, however his shot deflected tamely into the Australian international's arms.
With Palace on top, it was against the run of play that the visitors netted the game's opening goal. As James Tomkins failed to connect with a header intended for Vicente Guaita, Glenn Murray raced with the Eagles' centreback towards the goal-line. Deftly stretching out his leg, Murray hit the ball on the volley from the edge of the box past the Spanish 'keeper with Tomkins left flagging as the loser of their battle.
Looking to haul his side level, Wilfried Zaha was denied as he struck an effort from a crowded penalty area which Lewis Dunk deflected just wide of Ryan's goal. From the resulting corner, Tomkins sent a cleared ball back into the box which Jeffrey Schlupp hit emphatically on the rotation, though his effort bounced wide.
Minutes before the half-time whistle blew, Palace launched an assault on the Seagulls' box, but Batshuayi and James McArthur both squandered potential chances and the home side entered the break a goal down.
Opening the second half, Alireza Jahanbakhsh threatened the Eagles when he released a dipping shot at goal. Despite the ball's unnervingly bending flightpath, Guaita got two hands behind it and maintained the tight scoreline.
But Palace were determined to not let the visitors extend their league further and pulled themselves level when Davy Propper brought down Andros Townsend in the Seagulls' box. Stepping up cool as ever in spite of the interfering wind, Milivojevic buried his side's solitary goal to bring the Eagles firmly back into the game.
Nestling into the back of the net, the captain's spot-kick seemed to blow the match open and the Eagles looked like a side with lifted confidence playing with the backing of a vociferous, energised Selhurst Park.
But their sustained spell of possession didn't once seriously threaten Ryan's goal and Palace - along with their fans - were left frustrated as several promising runs fizzled out with defensive clearances or well-missed efforts.
Milivojevic came close to doubling his and his side's tally when he unleashed a shot just wide of goal, yet it was the visitors who were celebrating next when Knockaert picked up the ball from distance on the right and, having skipped his way closer to the box, launched an impressive shot into Palace's inner netting.
Looking to replicate his teammate's strike, Jahanbakhsh took aim and fired from 25-yards, but his effort dipped just over Guaita's bar.
In an attempt to steal a point at the death, Schlupp blazed over from 10 yards as the Eagles were left to concede defeat.
Palace: Guaita, Van Aanholt, Tomkins, Dann, Wan-Bissaka, Schlupp, Milivojevic, McArthur (Benteke 77), Zaha, Townsend (Meyer 77), Batshuayi.
Subs not used: Speroni, Kelly, Ward, Kouyate, Ayew.
Brighton: Ryan, Bernardo, Dunk, Duffy, Montoya, Propper, Stephens, Bissouma, Jahanbakhsh (Locadia 90+3), Murray, Knockaert (March 75).
Subs not used: Button, Bong, Burn, Kayal, Izquierdo.
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