Stockport ended a run of 12 consecutive league defeats with a gritty defensive display to hold the Cumbrians to a goalless draw at Brunton Park.
Both sides ended the game with 10 men after Carlisle's Scott Dobie and County Jabo Ibehre were red-carded.
It was a distinctly off-colour Carlisle who failed to pose any first-half threat to the league's bottom club and Stockport almost took the lead when Jemal Johnson turned sharply to fire into the side netting.
It took a fine reaction save by Adam Collin to prevent the visitors scoring a minute later when Ibehre tried to force home Danny Pilkington's cross from close range.
Carlisle's half-time change, bringing Dobie on up front in place of veteran midfielder, Graham Kavanagh, seemed to produce instant dividends.
The Cumbrians created a string of chances, Kevan Hurst going closest with a delicate lob, which had keeper, Owain Fon Williams, beaten all ends up as it struck the far post and rolled back across the face of goal.
It was Stockport's turn to hit the woodwork on the hour when Ibehre tried a snap-shot from the edge of the box, which glanced off the Carlisle crossbar.
Carlisle were reduced to 10 men in the 71st minute when Dobie saw a straight red for raising his hands to defender, Danny Swailes, after a challenge inside the box.
The Hatters followed likewise in the 81st minute when Ibehre was given his marching orders for a second yellow after clashing with Ian Harte.
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