Two first half goals from David Artell and Gregg Blundell put paid to Paul Simpson's side's hopes as they were unable to trouble a well marshalled Chester defence.
The home side's early pressure paid off on 11 minutes as a corner was headed goalwards by Michael Branch, Carlisle keeper Anthony Williams blocked the initial effort, before Artell followed in with a header right on the goal line.
It took until the 23rd minute for the visitors to threaten, but Brendan McGill's goalbound effort was well charged down by Scott McNiven.
Carlisle came back into the game after their sluggish start and Karl Hawley almost took advantage of hesitation by Luke Dimech, but the defender redeemed himself with a recovering challenge.
Five minutes before the interval, Chester doubled their advantage as Ryan Lowe sent Blundell clear, and the striker's left-foot finish was clinical, leaving Williams with no chance.
United captain Kevin Gray was almost punished for a defensive lapse as he ducked under a long ball, allowing Blundell clear on goal, but the striker's shot was blocked by the legs of Williams.
On the hour mark, the home side were unlucky as a directly struck free-kick from Ben Davies clipped the bar from 25 yards out.
The visitors barely threatened in the second period and had only a header from Glenn Murray as their one moment worthy of mention, as Chester comfortably held on for victory.