Wilfried Zaha got two of the five scored before the break with James Tomkins also finding the net for the hosts, but goals from Glenn Murray and Jose Izquierdo twice pulled Brighton back to within striking distance
The visitors pushed hard for an equaliser after the interval with Wayne Hennessey saving well from Dale Stephens and Glenn Murray failing to find the target from point-blank range, but Palace held on for the points
The win takes Roy Hodgson's team above Swansea into 16th in the table, just one point behind Chris Hughton's Brighton and, more importantly, six clear of Southampton in 18th
Brighton could not match Palace's intensity in the early stages and were lackadaisical in sending only one man for a short corner in the fifth minute
Luka Milivojevic wandered into the box and drilled a low shot from a tight angle that found its way under the body of Mat Ryan before being turned in from near the goal-line by Zaha
Another corner saw Palace double the lead inside a quarter of an hour as Tomkins lashed home left-footed off the legs of Ryan after a scramble inside the penalty box (14)
Brighton soon responded through a corner of their own as Lewis Dunk was left unmarked to head into the path of Murray, who volleyed the ball high into the net against his former club (18)
Palace's lead was restored midway through the first half when Ezequiel Schelotto elected not to track Zaha's run and the Palace hero headed in well from Milivojevic's lofted cross (24)
Just when Hughton's side seemed out of it again, Izquierdo pulled the visitors to within one after eluding Joel Ward on the left and tucking neatly beyond Wayne Hennessey (34)
It remained a feisty contest after the break with Dunk and Stephens both testing the patience of referee Andre Marriner and Brighton might well have snatched something late on
Firstly, Stephens struck a bouncing ball well with Hennessey doing brilliantly to save low to his right, and then Murray could not make the right connection with a left-wing cross
That was as close as Brighton came with Palace hanging on to take the points that leave both clubs well placed to renew their rivalry in the Premier League next season
 "I thought after our first-half performance, which was arguably one of the best performances we have given here since I have come to the club, it was a little unfortunate that we conceded two goals from the only two clear-cut opportunities that came their way
"Of course, that meant that in the second half, if they step up their game and play a few more balls forward into our penalty area, we would have to find a way to hang on to the victory
 I am very pleased that the players managed to do that
" "It was uncharacteristic
 We have been very good at corners
 It is not like us but it is very difficult to give those goals away and get something from the game
 We arguably had the best chances in that second half to get an equaliser or a winner but you can't give the goals away that we gave away in the early period of that game
"Milivojevic produced an impressive performance, controlling things for Palace in the middle of the park and providing two assists, but the sight of Zaha in full flow is just exhilarating
That is not news to Palace's supporters but for Zaha to find the net twice is a little rarer - this was the first time that he has done that in a Premier League game
 Good timing
The good news for Palace is that the remaining fixtures offer opportunities for points
 It is Watford away next Saturday, then Leicester at home and Stoke away before West Brom are the visitors to Selhurst Park on the final day of the season
Brighton are in action before all that when they play host to Hughton's old club Tottenham on Tuesday evening
 It is Burnley away next weekend before the trickiest of run-ins against Manchester United, Manchester City and Liverpool
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