The striker took his tally for the season 25 goals, cancelling out Ricardo Fuller's first-half opener for the Addicks.
Palace were top of the npower Championship shortly after Ian Holloway took over in October but a worrying dip in results had seen them slip off the pace.
They put in a shocking first-half display and were deservedly behind at the break, but Murray's brace secured only a second win in 10 matches for the Eagles.
Palace actually made a bright start with Wilfried Zaha, now officially on loan from Manchester United, running from his own half into the penalty area and forcing a last-ditch tackle from Chris Solly.
Fellow winger Yannick Bolasie then teed himself up for an extravagant overhead kick but his effort was saved by Ben Hamer.
But from then on it was all Charlton, with Fuller putting them ahead after 15 minutes.
The Jamaican frontman, who began his career at Selhurst Park, latched onto a long ball over the top, charged into the area and drove a low, angled drive through Julian Speroni's legs and into the far corner.
The Addicks should have been further ahead at half-time but Speroni saved from Bradley Pritchard and Johnnie Jackson.
Another former Palace man, Leon Cort, nodded over from under the crossbar after Speroni palmed Jackson's corner onto his head.
Jackson should have done better from Lawrie Wilson's cross but his header drifted high and wide.
As the break approached Palace did have another sight of Hamer's goal but Alex Marrow's shot was deflected wide.
Holloway sent on his new signing, veteran striker Kevin Phillips, after the interval and Zaha drove an early effort off target.
Bolassie forced a decent save from Hamer from outside the box and Stuart O'Keefe headed Zaha's cross wide.
Charlton had thrown away the lead to lose 2-1 against Sheffield Wednesday last weekend and the jitters struck again when Murray found the equaliser in the 75th minute.
The former Brighton frontman latched onto Dean Moxey's pass and tucked it past Hamer.
And four minutes later Palace grabbed their dramatic winner when Charlton failed to clear Stephen Dobbie's cross.
The ball fell to Jazz Richards, who teed up Murray for another expert finish past Hamer which clinched a vital three points for Holloway and his men.