Chasetown went a goal behind in the 7th minute as the home defence switched off and Ross Goodwin netted beyond Curtis Pond.
The hosts kept the pressure on their play off chasing opponents but failed to trouble keeper Jacob Carney.
Just before the interval the Scholars felt aggrieved that they weren’t awarded a spot kick for what looked like a foul on Levi Reid.
Pond made two top saves in the second half to keep the difference at one goal. First he denied Scott Ruthven and then low to his right from Josh Nodder.
Chasetown saw efforts from substitutes Liam Kirton and George Cater both stopped by Manchester United loanee Carney.
Stocksbridge doubled their lead in the 84th minute. Kurtis Turner drilled home beyond the dive of Pond from the corner of the penalty area.