Charlie MacDonald put them ahead on the stroke of half-time, Dean Bowditch added a second after the break and although Lee Miller scored on his home debut for Carlisle, Dean Lewington wrapped up the victory.
Early on Bowditch missed a couple of half-chances while ex-Middlesbrough striker Miller tested David Martin with a fierce drive at the near post.
However, it was the Dons who grabbed the lead in first-half injury time. Darren Potter floated a pinpoint cross in from the right and found MacDonald unmarked six yards out to lob the ball past the stranded Adam Collin.
Within two minutes of the restart Dons made it 2-0 with a sweeping move in which Adam Smith and Stephen Gleeson combined down the right. Gleeson’s cross gave Bowditch a simple finish at the far post.
Carlisle badly needed some inspiration and it came in the 52nd minute when Andy Welch won a free-kick just outside the area and Miller leapt highest in a crowded penalty box to head home James Berrett’s cross.
But the Dons once again exposed the frailties in the home defence in the 62nd minute when MacDonald’s clever lay off inside the box enabled Lewington to come bursting through and rifle a first time shot low past Collins.