And the margin of a morale-boosting victory might have been wider but for some first-half stops by visiting keeper Jon Worsnop.
Leigh managed just one on target shot all night, while Worsnop kept them in the game until two minutes before the break.
In just the first minute he tipped a 15-yard Chris Lumsdon shot round the post and he denied Derek Holmes, Chris Billy and Peter Murphy as Carlisle took a stranglehold on the match - forcing half a dozen corners in the first 18 minutes.
But when Worsnop could only parry a fierce drive by Lumsdon, Karl Hawley pounced on the loose ball to poach his first goal in seven outings.
After the break Holmes glanced a header just wide from a Murphy corner, as Carlisle continued to batter the Leigh defence.
And Worsnop tipped a dipping cross from Marc Tierney over the bar.
But, a minute after Carlisle brought on Brazilian Magno Vieira for scorer Hawley, the Cumbrians stretched their lead.
Big Leigh defender Leam Coyne brought down Holmes and Lumsdon drove the free-kick, from the right-hand corner of the area across the diving keeper and in off the foot of the far post.
Another free-kick produced Carlisle's third, Murphy stepping up this time to curl a 25-yarder in.
And with Carlisle rampant, Worsnop did well to deny Vieira, saving at the nippy striker's feet, before Brendan McGill contrived to miss a chance, three yards out, from a cross by the hard-working Murphy.
Afterwards, a relieved Carlisle boss Paul Simpson said: "It was a strong all-round performance. We kept battering away and had 10 shots on target in the first half.
"It was a no-win situation for us considering where Leigh are in the table and everyone expected us to turn them over, but they have won two and drawn two of their last six games, which is better than we have done and we knew it would be a tough game.
"There are signs that the belief is coming back that we can get into a play-off position."