First-half goals from Jeff Hughes and Neal Bishop set them on their way and further efforts from Francois Zoko and Jamal Campbell-Ryce after the break made it look easy against a Carlisle side that has only won once at home all season.
Although Carlisle began brightly it was County who made the early breakthrough when Jeff Hughes ghosted into the box to get on the end of Alan Judge's cross from the left. There were questions over the home defence's marking, but Hughes made no mistake, glancing a header neatly past keeper Mark Gillespie from six yards.
Good work by Jordan Stewart, racing down the left flank, led to County's second goal in the 27th minute. The fullback whipped in a low cross which Neal Bishop was on hand to poke past the stranded Gillespie from close range.
The Magpies looked a threat every time they went forward against a stationary Carlisle rearguard although Danny Livesey, with a shot which scraped the bar and Joe Garner, denied at close quarters by Bartosz Bialkowski, tried to provide a much-needed spark for the Cumbrians.
Substitute Francois Zoko was on target nine minutes after the interval, breaking away from Bradley Potts before slipping the ball past Gillespie from 12 yards, before Campbell-Ryce made it four from the penalty spot after being brought down by Chris Chantler.