The game seemed destined to end in a stalemate until substitute Jonathan Williams was brought down in the box by Lewin Nyatanga, with Murray finishing confidently to inflict a fourth consecutive league defeat on a beleaguered City.
Palace boss Dougie Freedman again had to do without defender Dean Moxey because of flu, while caretaker City manager Steve Wigley recalled Ryan McGivern to his starting XI after the defender missed the weekend 2-1 defeat at Peterborough because of a hamstring injury.
The visitors started brightly and enjoyed lengthy spells of possession but struggled to create any clear-cut chances.
Palace almost made them pay on 12 minutes when 18-year-old starlet Wilfried Zaha flashed a low drive wide of David James' left-hand post.
Zaha tested James four minutes later, but the former England goalkeeper was equal to it and parried the ball clear.
City continued to enjoy decent possession and created their first opportunity through Albert Adomah on 20 minutes, but the powerful striker could only lash his effort over the crossbar after muscling his way past Anthony Gardner.
The Eagles began to grow into the game as Zaha and Darren Ambrose started to pull the strings in midfield.
And it was former Newcastle man Ambrose who squandered the best chance of the half five minutes before the interval.
He could only lift his effort on to the roof of the net after James' wayward pass presented him with an open goal from 20 yards out.
Palace striker Sean Scannell also went close in first-half injury time, but fired over following neat interplay between Zaha and Glenn Murray.
Much like the first half, the early stages of the second was largely devoid of chances, with a couple of botched clearances from James in the City goal providing the only source of action.
The Palace fans thought they had a penalty on 63 minutes when Murray tumbled in the box following a shirt pull, but joy turned to despair upon realising the linesman was actually flagging the striker offside.
Brett Pitman missed the visitors' best opportunity 13 minutes from time, heading straight at Julian Speroni in the Palace goal after Adomah's ball in.
And that miss proved costly when Welsh Under-21 midfielder Williams, a 57th-minute substitute, drew the challenge from Nyatanga inside the area after being played in by Zaha.
The referee pointed to the spot, and Murray buried the subsequent spot-kick to clinch his fourth goal of the season and all three points for his side.