Leon Clarke was on target for the Spireites and handed brief hope to Sheridan, who starred for the Owls between 1989 and 1996, but it was not enough to prevent defeat as Gary Megson's side made it four wins in a row.
Lewis Buxton gave the home side a 17th-minute lead in the local derby when he met Ben Marshall's right-wing corner with a firm header.
Chesterfield enjoyed a good spell of possession at the start of the second half, Clarke putting a header wide before seeing a shot deflected off target. But Gary Madine sent Wednesday two-nil up when his low, angled shot beat Greg Fleming, who managed to get a hand to the ball but could not do enough.
Randall put a firm drive just over before Clarke found the net with a shot after the home defence had failed to clear Randall's corner with 10 minutes remaining.
Yet Marshall killed off any hopes of a Chesterfield revival when he beat Fleming with a low shot which the keeper appeared to have covered.