The Spireites had chances to win it, Marc-Antoine Fortune and Lee Shaw both presented with golden opportunities in the opening stages.
In the second half they had goalkeeper Shwan Jalal to thank when he made an impressive triple intervention to deny Barrow.
We rated the players' individual performances.
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Shwan Jalal - 8 - Equal to everything that came his way, including a one-on-one that led to two vital sliding challenges outside his area. Distribution, at times, the only downside to his performance.
Brad Barry - 6 - A solid enough all-round display until his unfortunate injury. Could be a big miss while he's out.
Jerome Binnom-Williams - 5 - Put in one terrific cross early on but struggled with his deliveries after that.
Haydn Hollis - 6 - Occasionally struggled with his distribution. Defensively, solid for the vast majority.
Will Evans - 6 - Guilty of, at times, picking the wrong option on the ball. But defensively sound.
Jonathan Smith - 6 - Looked to try and drive Town forward and keep them on the front foot. Chesterfield lost his presence from midfield when he had to move to right-back.
Robbie Weir - 5 - Perhaps the poorest he's been in possession since his comeback from injury. Wasn't able to play those raking balls to the flanks that have been so effective recently.
Curtis Weston - 6 - Tried to get forward in search of goals, got involved in attacks in and around the area.
Alex Kiwomya - 6 - Played his best football in the first half when space was open to him. Faded a little.
Lee Shaw - 7 - Should have scored early on. Did everything he could to make amends, put in a couple of great balls from the right and ran up and down all afternoon. Took a bit of a battering for his troubles, kept going.
Marc-Antoine Fortune - 5 - Missed a golden chance when he went one-on-one. Did okay up until his early injury, but Town should be getting more from him.
Tom Denton - 6 - Came on after 39 minutes and won the majority of his headers. Could have done better with a second half chance.