Carlisle have now shipped 13 goals in their first three league games and Coventry could have registered more but for a series of fine saves by home goalkeeper Mark Gillespie and some wasteful finishing.
City were two-up inside six minutes through Leon Clarke and Franck Moussa. Billy Daniels made it 3-0 at half-time and Clarke netted his second after the interval.
Coventry got off to a flying start with a fourth-minute goal by Clarke, who was given time and space to try his luck from 20 yards out. The striker's shot left Gillespie helpless as it flew unerringly into the top right-hand corner.
City were 2-0 ahead two minutes later, this time thanks to a solo effort by Moussa, who strolled through a static Carlisle defence before calmly chipping the ball over the diving Gillespie from inside the area.
Carlisle missed a chance to get back in the game after 15 minutes when Andy Webster shoved Mark Beck in the box. But Joe Murphy produced a fine save, diving low to his right, to keep out James Berrett's spot kick.
The Carlisle defence continued to be all at sea and it was no great shock when Daniels slotted home the Sky Blues' third goal in the 32nd minute after Callum Wilson had laid on the chance with his low ball from the right.
Just when Carlisle were starting to get a foothold in the game after the break, an error by on-loan Charlton defender Kevin Feely let in Clarke, who ran through to slip the ball past Gillespie.
Brad Potts luck was out when he caught Murphy off his line with an effort from inside his own half, the ball striking the inside of the post and bouncing clear.
But Coventry should have added to their tally but for a series of last ditch saves by Gillespie and the woodwork, which denied former Carlisle forward Mathieu Manset.