The southerners missed several chances in the first half but were rewarded for their domination six minutes after the break thanks to Mahamane Traore, who diverted a Nemanja Pejcinovic effort into the goal following a corner kick.
Didier Digard doubled their lead eight minutes later with a low strike following another set piece the Sochaux defence had failed to clear.
Argentine striker Dario Cvitanich wrapped it up with a fine lob seven minutes from time, his 14th goal of the season.
Nice provisionally climbed up to fourth on 54 points, level with St Etienne who occupy the third and final Champions League qualifying spot on goal difference.
Olympique Lyon, one point behind Nice in fifth, take on mid-table Toulouse later on Sunday.
Second-placed Olympique Marseille, who trail leaders Paris St Germain by 10 points on 57, visit Lille, sixth with 52 points, in the day's late fixture.
Sochaux, who did not have a single shot on target at Nice, stay fourth from bottom, one point above the relegation zone.