Plymouth Argyle 0 Crystal Palace 1
Teenager Moses, rated £5million and almost certain to leave Selhurst Park in the next fortnight, scored the Palace winner midway through the first half with a sublime piece of skill.
Latching on to defender Lee Hills' high and hopeful punt into the Plymouth penalty area, Moses dragged the ball down and wrong-footed the whole Argyle defence before firing home for a spectacular individual goal.
Argyle, who went into the game on the back of two successive league wins, made scant headway against former manager Neil Warnock's men in the first half.
Palace, four games unbeaten over Christmas, came within inches of stretching their advantage before the break when Gary Sawyer failed to clear properly.
Darren Ambrose seized on the loose ball and attempted to lob a shot from the edge of the penalty area over Romain Larrieu, only for the French goalkeeper to tip the shot over his crossbar.
Ambrose was again to the fore after the break on a surface that continual rain was beginning to make treacherous, extending Larrieu with a low shot from long range.
Despite the worsening weather, some decent football was possible, and Fallon's backheel played in Alan Judge for a shot that fizzed across the face of the Palace goal.
Palace, though, decided not take any risks with Moses, with Warnock withdrawing the goalscorer in favour of Calvin Andrew.
As the rain lightened, reducing the threat of a second abandonment at Home Park this season, Palace tightened their grip to leave Argyle still in deep trouble at the foot of the Championship table.