Christophe Galtier's men produced another excellent home performance at the Stade Geoffroy Guichard to secure a result that gives league leaders Paris Saint-Germain the chance to further extend their lead at the top when they host Marseille on Sunday.
Midfielder Fabien Lemoine opened the scoring for the hosts on 17 minutes as he fired home a sumptuous strike from the edge of the area after Monaco had failed to deal with a corner.
On loan Marseille forward Jordan Ayew put Sochaux ahead after 70 minutes, with striker Cedric Bakambu wrapping things up 12 minutes later as Herve Renard's men moved within five points of safety with their third win in five league games.
There was no such success for Valenciennes, who slipped below Sochaux by virtue of a 3-1 loss at Reims.
Substitute Gaetan Charbonnier's 77th-minute goal capped an excellent performance from Reims, whose only mistake came three minutes from time when goalkeeper Johnny Placide put through his own net.
