Palace started poorly and went behind in the opening five minutes for the second successive game when Lewis Dunk rose highest to head in a corner from Pascal Gross.
Roberto de Zerbi’s side dominated the ball throughout the first half and they doubled their lead in the 33rd minute when Jack Hinshelwood headed in Tariq Lamptey’s cross at the back post.
It got worse for the visitors a minute later when deadline-day signing Adam Wharton was caught in possession, and Gross teed up Facundo Buonanotte to score easily from close range.
Palace scored a consolation when Jean-Philippe Mateta headed in Joachim Andersen’s cross with 20 minutes to go before Joao Pedro restored the three-goal lead with an excellently worked goal late on.
Hodgson’s side failed to create many openings of note and Palace’s supporters once again expressed their frustration with the club ownership and management with banners calling for change.
Brighton, who made five changes from the side who lost 4-0 to Luton in midweek, looked rejuvenated.
The intensity they showed on the pitch was matched by their manager, who picked up his third booking of the season while appealing against a decision, and so will have to watch their next game from the stands.
Defeat for Hodgson puts Palace’s form back under the microscope. While they defeated Sheffield United last Tuesday, they have won just four of their past 17 league matches.
The Palace boss will point to the fact that he did not have his best players, with Eberechi Eze not fit enough to be in the squad and Michael Olise limping off just 11 minutes after coming on as a half-time substitute.