The Eagles, who only clung on to a place in the top six with a first win in 10 matches last weekend, managed to cancel out their arch-rivals in the first leg. But they surely face an uphill task when they head down the M23 for Monday's second leg after 30-goal top scorer Murray was stretchered off.
The former Seagulls striker collapsed in agony after appearing to get his studs caught in the turf in the second half, and his play-off campaign looks over.
In contrast to Palace, Brighton came into the game on the back of a nine-match unbeaten run. And it was clear in the first half which team was in form with Brighton opening up a nervous-looking Palace side with their trademark slick passing.
Wayne Bridge skipped past Joel Ward and crossed for Leonardo Ulloa six yards out, but the Argentinian striker headed wastefully wide.
Will Buckley's cross was then met by Dean Hammond in the area and the midfielder crashed a powerful header towards goal, but Julian Speroni made a fine point-blank save.
For Palace, the lively Jonny Williams drove narrowly wide while Murray could have had a penalty when Matt Upson held him in the area, but referee Michael Oliver was unmoved.
Wilfried Zaha was making his final home appearance for Palace ahead of his summer switch to Manchester United.
The winger was rarely allowed to show the talent which persuaded Sir Alex Ferguson to invest £15million in him, although one shimmy, run and cross deserved better than Williams' tame header.
Zaha found more space after the interval and turned Inigo Calderon inside out, and back again, before fizzing a low ball across goal which Murray just failed to get a touch on.
Then Owen Garvan's cross was met by Danny Gabbidon but his header was kept out by Tomasz Kuszczak, with Andrea Orlandi completing the clearance.
Palace's evening went sour when Murray tried to turn sharply in the box, crumpled to the ground and needed lengthy treatment before leaving the action on a stretcher.
Yet they almost grabbed a late winner from another Garvan cross which Kagisho Dikgacoi tried to bundle home, but Calderon was on hand to hack the ball clear.