Marc Pugh set the Cherries on their way with a first-half double and although Liam Noble replied for Carlisle, Lewis Grabban and Lee Barnard piled on the agony for the home side before David Symington grabbed the Cumbrians' second.
Carlisle gifted Cherries their early goal when Frank Simek failed to deal with Harry Arter's ball into the box and Pugh was able to waltz around goalkeeper Mark Gillespie and roll the ball into an empty net before Noble drilled a low first-time shot across David James for the equaliser.
Bournemouth's second goal in the 31st minute was again helped by poor defending as Simek was turned inside out by Pugh, whose effort from the tightest of angles squirmed over the goalline and the home defence opened up obligingly in the 52nd minute to allow Grabban to stride through and neatly slip the ball past the advancing goalkeeper from the edge of the box.
There was more defensive woe for the Cumbrians after 61 minutes when Barnard was given time and space in a central position just outside the penalty area and his low right-footed shot took a deflection to leave Gillespie wrong-footed.
Substitute Symington gave Carlisle a ray of hope with his first league goal in the 76th minute, blasting home from 12 yards after Robson's cross, but that was all it was for the home side.