Callum McGregor fired the Magpies ahead in the first half only for Matty Robson to equalise with a clever free-kick.
David Amoo's sixth goal of the season settled it after the break leaving County still in search of their first away win, although they threw everything at Carlisle late on when only a series of magnificent Mark Gillespie saves kept them at bay.
When Carlisle lost possession in midfield McGregor, County's on-loan Celtic midfielder, took full advantage as he drilled a low, 20-yard shot past Gillespie to find the bottom right-hand corner of the net and give his side a 27th minute lead.
A free-kick 25 yards out after Joss Labadie had fouled Amoo gave Carlisle the opportunity to level in the 41st minute. Robson's low shot from the left seemed to catch the Magpies' defence cold and Bialkowski could only watch as the ball zipped through a gap in the wall and in at the right-hand post.
The livewire Amoo put the hosts ahead in the 54rd minute, squeezing the ball home from a yard out close to the by-line after Robson's initial burst and shot had left County's rearguard at sixes and sevens.
Carlisle keeper Gillespie denied County with a stunning double save from Alan Sheehan's free-kick and Andrew Boucard's follow up effort, and was again Carlisle's saviour when he prevented McGregor grabbing a second.
Then when substitute Marcus Haber finally seemed to have him beaten the keeper somehow got his legs in the way of the shot.