Chasetown started brightly and home keeper Jacob Carney twice had to save from Liam Kirton and Josh Cooke.
The visitors were on top but fell behind against the run of play. A throw in from Jordan Lemon found its way across the box and when Curtis Pond saved the first shot, Luke Mangham followed up to scramble the ball over the line.
Pond then made a super save to deny a volley from Ross Goodwin at point blank range.
The Scholars had the frame of the goal to thank for the scoreline staying 1-0. Josh Nodder hit the cross bar from long range.
Chasetown deservedly levelled just before half time when George Cater rounded the keeper and slotted past the defender on the line.
Cater thought he had made it 2-1 when he slid the ball past Carney only to be ruled out for offside.
The hosts conceded 9 minutes into the second half, Carney sliced a clearance and Jack Langston sent it goalwards with the open goal gaping, nestling just inside the keeper’s right hand post.
Steels were under pressure for a while and Langston and Josh Cooke had further chances.
Stocksbridge levelled though after a sustained spell of pressure from themselves and after Pond saved well, Lewis Whitham tapped home the rebound.
Chasetown regained the lead in the 90th minute. After a Jimmy O'Neill long throw in caused havoc in the home penalty area, Ryan Wynter and Kirton both had stabs at the ball and eventually Langston drilled it hard and low and a deflection wrong footed Manchester United youth keeper Carney.