The Spireites led two-nil after 21 minutes thanks to goals from Kabongo Tshimanga and Akwasi Asante.
But the game swung on a red card for Jeff King early in the second-half and the hosts made them pay with two goals from Will Collar and Ryan Croasdale.
It seemed only a matter of time before the Hatters went in front but the Blues battled well and managed to come away with a creditable point.
The result means Stockport stay top and one point clear of Town but Danny Webb’s men have a game in hand.
Here are Liam Norcliffe’s player ratings from the game...
Scott Loach 6
Couldn’t have done much about either of Stockport’s goals. Despite the hosts’ pressure in the second-half he was not really tested.
Fraser Kerr 7
He was on the ropes at times with Stockport’s direct players but he kept battling and he was particularly good in the air when he moved into the middle of the defence when Croll went off injured in the second-half.
Jamie Grimes 9
Just edges out McCourt for my man of the match. He was a man mountain at the back. He really stood up to the challenge and hardly missed a kick. Dominant in the air and he got Town out of a couple of tricky spots with some last-ditch tackles and clearances.
Luke Croll 7
Another solid display from the captain but sadly his night ended in injury and he left the stadium on crutches.
Jeff King 6
Sent off early in the second-half with Chesterfield two-nil up. It was a strong tackle and he appeared to win the ball but perhaps the referee felt he caught his man with the follow-through. The red card swung the game.
Manny Oyeleke 7
He was dictating play for the visitors in the first-half and provided the assist for Tshimanga’s goal with a lovely dinked pass. But sadly he was forced off injured with 20 minutes to go.
Jak McCourt 8
A second successive strong performance. He got a foot in, played some nice passes and really dug deep when Town went down to 10-men. He was a warrior in the final 25 minutes.
Alex Whittle 8
He never stopped running all night. He played with his heart on his sleeve, pressed and harried the opposition and showed great determination as the clock ticked down.
Liam Mandeville 8
An absolute workhorse all night. Put in a proper graft and did very well to keep tracking his runners and tackling back when he was moved out wide right.
Akwasi Asante 7
Put Chesterfield two-nil up with a low, driven shot from the edge of the box. He was causing the hosts a lot of problems in the first-half as he kept drifting out wide left. He was subbed off after King’s red as they shuffled the pack.
Kabongo Tshimanga 7
Scored a brilliant volleyed opener for his 25th goal of the season. He was feeding off scraps after King’s red but he kept working and did his defensive work.
Tyrone Williams 7
Came on for Asante and went into the backline. Won a lot of headers as Stockport repeatedly kept pumping balls into the box.
Jim Kellermann 7
Came on for the injured Oyeleke on 70 minutes and gave them some fresh legs in midfield.
Calvin Miller N/A
Replaced the injured Croll late on.