Albion were looking to bounce back after a run of three games without a win.
After a scrappy start to the game, it was the visitors who struck first after 27 minutes with Trevor Chalobah heading in from a corner – which was not defended at all well by Albion.
Bart Verbruggen was kept busy as Palace threatened to double their lead, which they managed to do when Tyrick Mitchell’s inch-perfect cross was headed in at the back post by Ismaila Sarr after 33 minutes.
Tariq Lamptey didn’t cover himself in glory for this goal, as he was beaten easily by Mitchell out wide after a long ball forward.
The full-back was replaced at half-time by Julio Enciso, who has had limited game-time for the Seagulls this season and has been linked with a January loan move.
He nearly made an instant impact on this game, though, as the Paraguay international played a one-two with Carlos Baleba and forced Dean Henderson into a superb save at full stretch.
Lewis Dunk and Kaoru Mitoma also went close as Albion piled on the pressure in the second-half but Palace managed to weather the storm.
It was the Eagles who had the ball in the net a third time but it was ruled out for a foul on Pervis Estupinan.
Oliver Glasner’s side were not to be denied a third goal, though, as Sarr put the icing on the cake with a calm finish after some terrible Albion defending.
This capped off a thoroughly disappointing day for Fabian Hurzeler’s men, who did grab a consolation through a very scrappy Marc Guehi own goal but it did little to lift spirits inside the Amex.
The 3-1 defeat leaves Brighton ninth in the table after four games without a win.
Scroll down and click through to see our Brighton player ratings:
5. Jan Paul van Hecke - 5
Not how he would have wanted his 50th Premier League appearance to go. Perhaps could have defended the corner better for the first goal. Caught out on the half-way line at 1-3 but Palace somehow failed to score a fourth. Photo: Mike Hewitt/Getty Images
6. Pervis Estupinan - 5
Not able to impact the game as much as he would have liked this afternoon. Got lucky after he dallied on the ball under pressure from Sarr, who was penalised for a foul, as Palace won the ball and scored. Photo: GLYN KIRK/AFP via Getty Images
7. Yasin Ayari - 5
Not one of his better performances. Didn’t have control of the midfield Photo: GLYN KIRK/AFP via Getty Images
8. Carlos Baleba - 7
One of the better performers on the afternoon. Showed his class in moments and was key to a bright start to the second half. He, and his manager, were fuming after the referee blocked his path before the corner which led to the first goal and didn't stop play. Photo: GLYN KIRK/AFP via Getty Images