The game-changing moment came after just eight minutes at Selhurst Park as Seagulls defender Lewis Dunk lost possession and saw red for bringing down the impressive Yannick Bolasie.
Owen Garvan hit the resulting free-kick against the crossbar but it was only a matter of time before the dominant Eagles broke the deadlock as Murray, who switched between the fierce rivals 18 months ago, headed home Bolasie's corner.
Craig Mackail-Smith should have levelled matters immediately after half-time but could only hit a post when clean through, and the miss proved crucial as Tomasz Kuszczak brought down Murray in the penalty area and the striker stepped up to fire home his 17th goal of the season from the spot.
Matters went from bad to worse for the Seagulls in the 71st minute as Gordon Greer fouled Murray in the area, and with the Palace striker having previously missed two penalties this season when looking for a hat-trick, it was Garvan who converted from 12 yards.
Close to 50 miles may separate the two sides, who had only met six times in the past 10 years before this, but that will not ease the pain of defeat for Brighton, who have also seen their seven-match unbeaten run come to an end.
Impressive Palace, meanwhile, have now lost only one of their last 17 and are unbeaten on home soil since the opening day, with Eagles fans able to enjoy top spot for at least 24 hours until second-placed Cardiff host Sheffield Wednesday on Sunday.