The Grecians dominated from the off and without the agility of home keeper Matty Glennon they would have had the game sewn up at half-time.
The goal when it came early in the second half, was gifted wrapped by the home defence.
Glennon called to claim a cross, but with four United defenders waiting for their keeper to come, Steve Flack stole into loop a header into an empty net.
Exeter doubled their lead in the 63rd minute from a corner after Gary Sawyer's header was deflected on to and over the bar.
Alex Jeannin's subsequent corner was flicked on at the near post and Lee Phillips leapt highest at the far post to head in from two yards.
Glennon's first-half saves had left the Devon side frustrated at the break.
Twice he kept Philips at bay, first from a point-blank header and then from a 12-yard shot.
By contrast Carlisle effectively gave Grecians keeper Paul Jones the day off.
The only time the Cumbrians threatened was through sub Glenn Murray and although his clever flick beat Jones, it rebounded back off the woodwork.