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...
1. Scott Loach 7
This was his seventh clean sheet of the season. He saved from Eastleigh's Harry Pritchard in the first-half but other than that Town's defence protected him well. He took the pressure off in the final seconds with a great catch from a set-piece delivery. Photo: Tina Jenner
2. Fraser Kerr 8
He is in fine form right now. This was another solid defensive performance from him. One back-pass to Loach in the first-half caused Chesterfield a problem and he probably went long a bit too much in the second-half but he wasn't the only one. Photo: Tina Jenner
3. Gavin Gunning N/A
Unfortunately his night ended after just 10 minutes after he suffered a broken nose following a boot to the head. Photo: Tina Jenner
4. Laurence Maguire 8
Expertly defended the 18-yard box and was tidy enough in possesion. No surging runs forward like against Boreham, but it wasn't that type of game. Came close to scoring in the second-half with a header. Photo: Tina Jenner