Tshimanga smashed in a penalty on 16 minutes after Liam Mandeville was brought down in the box.
The striker then grabbed his second in the first minute of the second-half as he tapped home from George Carline’s assist.
The results means the Spireites have won all three of their matches this season and have not conceded a goal.
Here’s Liam Norcliffe’s player ratings from the game...
1. Scott Loach 7
A third successive clean sheet. He made a couple of good saves in the second-half, one of which came about after he miss-kicked a back-pass by Gunning so he made up for that slight error. Photo: Tina Jenner
2. Fraser Kerr 8
A solid performance for the second time in three games. Nothing got past him. Had to come off late on with a cut to the head. Photo: Alan Palmer
3. Gavin Gunning 8
Immense. His best display of the season so far. Didn't miss a header. Photo: jason chadwick
4. Laurence Maguire 7
Played a big part in the second goal with a diagonal ball to the far post which Carline headed back across to Tshimanga. Linked up well with Miller down the left in the second-half as Chesterfield piled on the pressure. Got caught out once or twice with passes in behind him late on but overall he was good. Photo: jason chadwick