Palace took the lead from a corner as it was played short to Ruben Loftus-Cheek who fizzed cross hit the arm of Mathew Ryan and was tapped over the line by Wilfred Zaha.
Things got better for the hosts when James Tomkins tapped home after sloppy defending from another corner by Brighton.
Brighton pulled one back in the 18th minute when Pascal Gross's corner found Lewis Dunk who headed towards goal and top scorer Glenn Murray flicked it in off the underside of the bar.
Palace then made it 3-1 when Luka Milivojevic's floated ball picked out Zaha who nodded past Ryan.
The Seagulls then pulled another back again to make it 3-2 in the 39th minute when Jurgen Locadia played a ball in behind Andros Townsend and picked out Jose Izquierdo who calmly curled his effort into the bottom right corner.
Below are the lessons Brighton can learn from the game.
Marking was poor
For all three of Palace's goals, Brighton marking was poor. They failed to mark Loftus-Cheek for the first goal, then for the second they failed to pick up Tomkins and for the third, they did not mark up on Zaha.
This ultimately cost them as with better marking you would hope not to concede one, if not all three, of the goals that Palace scored on Saturday afternoon.
Add to this Brighton gave Palace too much time on the ball it really hampered their chances of getting something out the game.
Murray failed to take two of his chances
Despite scoring one goal, Murray will feel he could have had a hat-trick if he would have scored two golden chances.
The first came when Izquierdo closed down the palace defender and the blocked pass fell to Murray five yards out and instead of shooting first time he took and touched and his shot was blocked.
The other came when a cross was curled into him and he couldn't sort his feet out when if he had it would have ended up in the back of the net.
However, his finish for the goal was a poacher's finish he had the know how to see where the gap between the defender on the line and the goalkeeper was and flicked the ball into it.
The left side did really well for The Seagulls
One positive note was that Brighton's left side did a great job throughout the game.
Gaetan Bong got up and down the left flank and put some good balls in to the box and defended really well against a tricky winger in Townsend.
Izquierdo looked very threatening on the ball and produced a fine finish for the goal as well as long very dangerous whenever he got the ball due to him looking to drive at the Palace defence and get Brighton on the front foot.