There was no fairytale beginning for new City boss Mark Robins as the Sky Blues fell to a fifth consecutive league defeat at home to the Cumbrians
Danny Cadamarteri converted from the spot after 23 minutes but David McGoldrick levelled things up with eight minutes of the first half to go with a delicate header at the back post.
Danny Livesey netted the winner for the visitors though with a header of his own ten minutes after the restart.
Robins marked his first game in charge of the Sky Blues by making four changes to the side that lost in midweek to Shrewsbury.
Gary McSheffrey, Bill Daniels, Reece Brown and John Fleck all came back into a side which also included new loannees Conor Henderson and Jamie Reckord on the bench.
The gane started in a scrappy fashion with plenty of tackles and strongly contended 50/50's.
It took until 16 minutes for the first real chance of the game to present itself though and it wnet the Sky Blues' way as McGoldrick bustled Danny Livesey off the ball and cut a pass back across the six-yard box across the goalline for Gary McSheffrey who only needed the slightest of touches to guide the ball into the net and missed contact by inches.
It was the visitors who took the lead though after 24 minutes after Richard Wood brought down Cadamarteri in the area, leaving the referee to point to the spot and Cadamarteri to convert past Joe Murphy.
City were nearly level just three minutes later when a neat bit of one-touch football between John Fleck, Carl Baker and McGoldrick saw Baker shoot from the egde of the area with the ball spilling away from Carlisle 'keeper Mark Gillespie and towards the waiting Fleck and McGoldrick, the ball narrowly avoiding both of them.
Fleck went close again with nine minutes of the half to go when his effort from distance was deflected just over the bar.
The Sky Blues got their just desserts just moments later though when a beautifully lofted deep cross from Baker found McGoldrick at the back post to nod a delicate header back across the face of the goal and just
inside the far post.
The Sky Blues started the second half brightly as well when Baker cut inside the left back and fired a shot just inside the near post, Gillespie tipping the ball around the woodwork.
Joe Murphy was then required to make a smart save on 55 minutes when Reece Brown's headed clearance only went as far as Jon-Paul McGovern who hammered a half volley from just inside the area which the City 'keeper parried away.
Carlisle found themselves infront again from the resulting corner though when Livesey connected with the deliver and sent a header just inside the near post.
The Sky Blues gathered themselves after going behind for a second time and Fleck went close with 20 minutes to go when his low shot was deflected just wide.
McGoldrick then went close to a second with ten minutes to go when he latched onto a through ball from Kevin Kilbane and shot across Gillespie but hit the foot of the far post.
Substitute Cody McDonald then hit the other post with three minutes to go when a long, deep cross from the left from Fleck picked out the striker whose first touch guided the ball past Gillespie but against the foot of the woodwork.
The opportunity summed up the afternoon for City who came a whisker away from adding to their tally on a number of occasions only to miss out by inches as Carlisle saw out the game to claim all the points.
Attendance: 10,674 (951 away)
Coventry City: Murphy, Clarke, Wood, Brown, Kilbane (c), McSheffrey (McDonald 69), Fleck, Baker, Daniels (Reckord 64), Jennings (Henderson 22), McGoldrick
Subs: Dunn (GK), Elliott, Edjenguele, Willis
Carlisle United: Gillespie, Simek, Robson, McGovern, Livesey (Edwards 87), Muprhy, Cadamarteri, Thirlwell (c) (Potts 81), Berrett, Garner (Higginbotham 83), Chantler
Subs: Collin (GK), Noble, Beck, Symington
Bookings: Baker (COV) Thirlwell (CAR)