Palace thought they had got off to the perfect start when Jazz Richards put the ball in the net after playing a neat one-two with Murray, only to see his effort ruled out incorrectly for offside.
Palace were denied a goal yet again, this time by the crossbar as Yannick Bolasie saw his bicycle kick crash into the frame of the goal.
Ian Holloway's side finally took the lead when Murray volleyed home Mile Jedinak's free kick at the back post to score his 28th goal of the season.
The visitors were looking the better side in the second half but it was Palace who doubled their lead in the 66th minute as Stephen Dobbie curled a free kick into the top corner from 25 yards.
It was nearly three for the home side as Dobbie's header found its way to substitute Kevin Phillips, who volleyed at goal first time but saw his effort clatter the crossbar.
There was a late consolation for Sean O'Driscoll's side as Jonathan Parr headed into his own net but Palace held out to secure the win.