In a tight encounter with very few chances, the hosts edged it through strikes from James Jennings and Alex Reid.
It has still been a fairly good week for Town who have collected six points from a possible nine after coming out of isolation.
The loss leaves the Spireites in 16th in the National League table, seven points off the play-offs.
Here are Liam Norcliffe’s player ratings from the game...
1. Grant Smith 6
Not a lot Smith could do about either of Stockport's two goals, the first he has conceded in a Town shirt. Made a smart stop to save Tom Walker's free-kick in the first-half. Photo: Dean Atkins
2. George Carline 6
Carline was not at the same high standards we are used to seeing. In fairness, Stockport did not allow Town many opportunities to get the ball to him. He had a decent chance at the far post just before half-time but fluffed his lines. Photo: Dean Atkins
3. Will Evans 6
The skipper put in a fairly decent showng. He was strong and dug in. Had a chance inside the box at 0-0 from a corner but blazed it well over. Photo: Dean Atkins
4. Haydn Hollis 6
Made some good clearances in the first half and did okay overall. Photo: Dean Atkins