First-half goals from Alex Whittle and Kabongo Tshimanga secured the victory after the hosts had Kyle Storer sent off.
Town had chances to add to their lead and restricted the Moors after the break to bring the three points back to Derbyshire.
The win means the Blues have lost just one in 16 games and are unbeaten in nine.
Here are Liam Norcliffe’s player ratings from the match...
1. Scott Loach 7
His ninth clean sheet of the season. He made a crucial save from Rooney just moments before Tshimanga doubled the lead. His kicking was a bit off at times. He had little to do after the break although there was one hairy moment with a back-pass. Photo: Tina Jenner
2. Tyrone Williams 8
An accomplished performance on his return to his former club. Barely put a foot wrong and made a great block just before Tshimanga scored the second. Photo: Tina Jenner
3. Jamie Grimes 8
A smooth performance in the middle of the back three. Stayed calm and composed and never looked in danger. A really good display from him. Photo: Tina Jenner
4. Luke Croll 8
Another solid showing. Made a key intervention to cut out Cranston's diagonal ball over the top in the first-half. Nice and steady after the break. Continues to impress since signing. He was on the end of a nasty tackle from Storer which resulted in a red card but thankfully he was not seriously hurt. Photo: Tina Jenner