James Berry scored his first goal in two months when he blasted in off the post on 62 minutes after Lee Bonis forced a mistake from home goalkeeper Wyll Stanway and that turned out to be the winner in Cumbria.
The results means the Spireites, who stay seventh in League Two, have won all of their last three matches and kept clean sheets in all of them.
Here are our player ratings from the game...
13. Lee Bonis 7
Lee Bonis 7 On for Dickson at half-time and his work-rate forced a mistake from Barrow goalkeeper Stanway which allowed Berry to take advantage. Came close to adding a second goal late on. Photo: Brian Eyre
14. Dilan Markanday 7
Dilan Markanday 7 On for Mandeville on 72 and he was lively. Had a chance to double the lead but his shot was blocked. Photo: Tina Jenner
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