Shefki Kuqi looked to have secured Palace a point in the 75th minute after Chris Cohen's inswinging free kick had given Forest a half-time lead, but Matt Thornhill's comical winner eight minutes before the end sealed the away side's first away win of the season.
Forest started much the brighter and should have taken the lead inside two minutes after Robert Earnshaw was presented with the freedom of the penalty area only for his firm strike to be tipped over by Julian Speroni.
Calderwood's side hammered home their dominance in the 27th minute after Cohen's left-footed free-kick from 40-yards eluded everyone including Speroni to creep in at the back post.
Paul Ifill went close to equalising five minutes later, before Earnshaw missed a glorious chance moments before the break.
Ifill missed another great chance straight from the restart after latching on to substitute Kuqi's knockdown only to scuff his effort wide as Palace begun the second half quickly
Ben Watson somehow contrived to shoot wide from three yards after Ifill's cut back in the 55th minute as Palace continued to press.
And the Eagles were rewarded for their much improved second-half display after Kuqi smashed home from the edge of the box in the 76th minute.
But in comical circumstances Forest claimed the winner eight minutes from time when Speroni was forced into a superb save from Perch after the midfielder was slid through by Lewis McGugan.
But Palace made a hash of clearing the rebound and somehow Matt Lawrence's attempted clearance off the line fell to Forest substitute Thornhill, whose effort was going wide before clipping the heel of Eagles debutant Rhoys Wiggins to roll into an empty net.
Forest midfielder McGugan missed a great chance to seal the points in stoppage time, but the away side held on to ease their relegation fears.