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:
9. Kaoru Mitoma - 6
Early effort saved from close range. Had another chance from Minteh’s pass but couldn’t make space for a shot. So close to halving the deficit. Looked the most likely source of a goal when Albion put the pressure on. Photo: Alex Pantling/Getty Images
10. Yankuba Minteh - 5
Some flashes of what he can do out wide and created a chance for Mitoma. His impact faded as Palace took control. Photo: Mike Hewitt/Getty Images
11. Joao Pedro - 6
Brilliant piece of skill with an overhead pass to set up Mitoma’s early chance. Frustrated with his teammates’ movement after wasteful cross. Shot blocked a Albion pile on the pressure in the second half. Trying to unlock the door but his passing not always at its best by the Brazilian’s standards. Photo: GLYN KIRK/AFP via Getty Images
12. Georginio Rutter - 5
Very quiet. Wasn’t able to impact the game in an attacking sense. Photo: GLYN KIRK/AFP via Getty Images