After a close and fairly uneventful first 45 minutes, the Spireites pushed the hosts back and came away with a deserved three points in the end.
Danny Rowe gave the Blues the lead from the penalty spot after debutant Jeff King was fouled in the box.
And four minutes later fellow debutant Tshimanga doubled the lead with a clinical finish.
Here’s Liam Norcliffe’s player ratings...
1. Scott Loach 7
A first clean sheet on his debut. He was not called into action too much but he was a calming presence at the back. Photo: Tina Jenner
2. Jamie Grimes 7
The left-footer played on the right of a back three which is not his natural position but has played there in pre-season. He was understandably a little uncomfortable on the ball in the first-half but he improved after the break. He was good in the air. Headed a cross over in the first-half and had a goal ruled out for offside at 0-0 in the second-half. Photo: jason chadwick
3. Gavin Gunning 7
The skipper was solid in his defensive work. Perhaps could have done better in possession in the first-half as he went long too often. Photo: jason chadwick
4. Laurence Maguire 7
Steady and reliable. Like Gunning, might have done better in possession at times. Photo: Rachel Atkins