Chesterfield dominated play but could not find a way past a stubborn and well organised away defence.
Town goalkeeper Kyle Letheren was the hero in the end with two saves in the shootout.
The Blues picked up £4,500 in prize money for winning the the tie.
The draw for the next round is at 1pm on Monday.
Here are Liam Norcliffe’s player ratings from the game...
The Blues picked up £4,500 in prize money for winning the the tie.
4 / 4