Minutes earlier, Keogh had a chance to put Carlisle in front but he flashed a header wide from a Graham Kavanagh corner. United had another chance in the 12th minute, after Matty McNeil went through Joe Anyinsah to give the Cumbrians a free-kick on the edge of the box, but Danny Graham pulled his shot wide of the post.
A crucial Keogh interception stopped Stockport adding a second in the 16th minute after Blizzard broke down the left and O'Grady threatened to score. O'Grady came even closer with a header from a Tommy Rowe corner when he was denied by the woodwork from six yards.
Keeper Williams saved Carlisle in the 41st minute when Oli Johnson was clear through on goal, but the United stopper saved his shot. Carlisle tried to level before the break but Graham wasted a good chance, putting a header wide of the post and Anyinsah flashed a header over from another excellent Cleveland Taylor delivery.
Anyinsah had another effort blocked just after the break as United went in search of the equaliser and it finally came in the 53rd minute, when former Preston winger Lewis Neal drilled a shot into the bottom corner. Stockport broke with Blizzard, who crossed for Tommy Rowe, but with the goal at his mercy the ball got stuck under his foot and the chance was gone.
Matty McNeil's last-ditch headed clearance then denied Graham, before Rowe grabbed the winner, stabbing home the rebound after Williams had parried his initial header. Carlisle then huffing and puffing for a second equaliser in the game in the last 20 minutes but they never looked like getting past County keeper Owain Fon Williams again.