Goals from Jeff King, Nathan Tyson, Liam Mandeville and Stefan Payne eased the Spireites to victory at the Tameside Stadium.
Town were in control and untroubled for most of the game as they saw off the National League North side.
They now advance to the next round where a potential tie against a Football League club could be waiting.
Here are Liam Norcliffe’s player ratings from the game...
1. Melvin Minter 6
A clean sheet on his debut. He had a very comfortable afternoon between the sticks with just one easy save to make early on. Photo: Jason Chadwick
2. Fraser Kerr 8
He handled the big, physical Hobson very well. He was dominant in the air and was in the right position numerous times to clear balls into the box. Photo: Tina Jenner
3. Jamie Grimes 8
A commanding performance in the middle of the back three. Picked out Tyson with a good through-ball for the second goal. Photo: Tina Jenner
4. Laurence Maguire 8
Defensively sound and his excellent deep cross from the left created the first goal. Photo: Tina Jenner