Peter Halmosi ended a run of four successive home draws for the Pilgrims to heap the pressure on Palace manager Peter Taylor.
The Hungarian international winger struck five minutes after the interval to score a dismal game's only goal.
If the game never hit the heights, the strike was of the highest quality, with Halmosi timing his volley of a sharply dropping ball to perfection.
The chance had come when Lee Hodges, recalled for his first league start of the campaign, hoisted a cross into the Palace penalty area.
Although the Palace defenders cleared the immediate danger, the ball fell nicely for Halmosi, whose shot was helped over the goal-line by visiting defender Tony Craig.
In a match of few chances, neither side looked capable of breaking the stalemate until Halmosi's intervention, and there were precious few goalscoring chances after the winner, either.
The best opportunity of the first half fell to Argyle's recalled striker Nick Chadwick, who had scored against Palace the previous three times he had faced them, but his header from Barry Hayles' precise cross was brilliantly tipped over by Palace goalkeeper Julian Speroni.
Palace responded with midfielder Danny Butterfield crossing from the right, but on-loan striker Besian Idrizaj wasted the opportunity when his header failed to extend Argyle goalkeeper Luke McCormick.
Just before the interval, Halmosi's doggedness saw the ball break to Chadwick ten yards from goal, but he could only hit the ball straight at Speroni.
Taylor introduced Republic of Ireland international Clinton Morrison at half-time, withdrawing Idrizaj, and threw big centre-back Leon Cort up front in the final ten minutes but the Pilgrims easily saw off Palace's ineffective efforts.
The defeat will increase speculation that Taylor's time at Selhurst Park is approaching an end, with Neil Warnock, ironically a former Argyle manager, waiting in the wings.