The City Ground club remain firmly rooted in the relegation zone as their inability to score extended to a fourth consecutive league game.
Despite enjoying the better of play in the first half, Steve Cotterill's men were unable to make the breakthrough, with Murray's pinpoint strike 10 minutes after the break proving sufficient to give the Eagles a much-needed first win in eight games.
In a first period devoid of clear-cut chances, Murray carved out a solid opportunity with only four minutes played.
With the ball pushed forward after Julian Speroni's long kick, Murray dug out a 25-yard drive that Lee Camp could only parry at full stretch.
Forest responded through Paul Anderson, the ex-Hull trainee drilling with force at an unguarded Speroni, only for Anthony Gardner to make a brave block.
Cotterill's charges, restricted to long shots by the wary Palace defence, could have been celebrating in the 15th minute if not for the good work of Wilfried Zaha.
Garath McCleary looked up to pick his spot from distance, but Zaha intercepted his ripping strike to diffuse the danger.
The hosts suffered an early setback when Wes Morgan went down injured in the 20th minute, Andy Reid his replacement.
Unabashed by the unforeseen change, McCleary summoned up another dangerous drive, this time after surging down the left wing, but Speroni was on hand to punch the ball clear.
Eagles manager Dougie Freedman, who spent two seasons as a player at the City Ground, kept faith with the containment strategy after the break that had kept his side alive in the first half.
With the onus on the Reds to push forward for a win that would propel them out of the relegation zone, Freedman's sole concern was avoiding a fourth consecutive league defeat on the road.
Cotterill, therefore, placed the emphasis on exploiting set-pieces, and first half substitute Reid nearly caught Speroni unaware with a wildly swinging corner.
But when Lee Camp's goal kick fell short to a lurking Zaha, the 19-year-old weaved down the right channel to pick out Murray in the penalty box.
The former Brighton frontman twisted to put his weight behind a clinical strike which beat Camp to break the deadlock.
With a first victory in eight games in sight, the Eagles continued to squeeze the home forwards into conceding possession.
Lewis McGugan and Dexter Blackstock, making his first appearance since November last year, were introduced for Anderson and Radoslaw Majewski with 20 minutes remaining in a last throw of the dice.
The tactical switch almost paid dividends in the 77th minute as McGugan rose to meet another inswinging Reid corner but he glanced narrowly over the crossbar.
Zaha miscued high and wide as the game entered the final phases, with Forest captain Luke Chambers heading harmlessly off target at the other end.
And Blackstock was denied a dream return to action when Speroni plucked his bullet header out of the air in added time.