Tshimanga bagged his 11th goal of the season from close-range after Stefan Payne squared the ball for an easy finish.
It was a tight, scrappy encounter in blustery conditions with neither side creating many chances.
Victory for the Blues keeps them in second but they are now just one point behind leaders Grimsby.
Here are Liam Norcliffe’s Chesterfield player ratings from the game...
Victory for the Blues keeps them in second but they are now just one point behind leaders Grimsby.