County took a 45th minute lead after soaking up a barrage of pressure from the visitors, when leading scorer Warren Feeney netted his 12th goal of the season to give the Hatters the advantage at the break.
But it took Chesterfield just six minutes of the second half to level matters when striker Mark De Bolla fired home after a clever flick on from Caleb Folan.
And it soon got better for the visitors when Mark Allott fired home with a 30-yard thunderbolt which left County keeper James Spencer no chance nine minutes from time.
County had their fair share of the chances and midfielders Keith Briggs and on-loan Kevan Hurst also went close, both with efforts that flew inches wide of the post.
But however hard the home side pushed they could find no way through Chesterfield's solid defence.
Boss Turner praised his team afterwards but admitted: "It's like trying to stop a train hurtling down the tracks with no brakes."
County remain rooted to the foot of the table and even with 12 games remaining look unlikely to avoid the drop.
Turner added: "I take great heart from what I'm seeing, but when you're rooted to the foot of the table it's very hard to get off the bottom.
"I thought our second-half performance was what I was looking for. We had more chances, more shots and were unlucky to lose.
"But sometimes you hold your hands up as a manager if it doesn't go your way."
Chesterfield assistant-manager Lee Richardson was delighted with his team's three points but also paid tribute to Stockport for piling on the pressure in the second half.
"Stockport got in some quality crosses after the break and they put us under fantastic pressure," admitted Richardson.
"But the amount of chances we created made sure we were always going to win.
"We just needed the three points tonight after the weekend, when we didn't do ourselves justice when we lost an important derby match. We played much better tonight and getting full points is the most important thing."