It was the first time Palace had kept a clean sheet this campaign, but they also missed the game's best chances, as home keeper Mathew Ryan made a fine double save to deny Christian Benteke and Wilfried Zaha in the 14th minute.
Brighton, who stretched their unbeaten home run to six games, were restricted to several half-chances in the opening 45 minutes, while Palace keeper Wayne Hennessey did well to parry a curling shot from Jose Izquierdo.
Former Palace striker Glenn Murray went close to snatching a late winner for Brighton when his header was cleared off the line by a defender, as the visitors were forced to hang on in the closing stages.
(Writing by Zoran Milosavljevic; Editng by Toby Davis)
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