Leon Clarke's goal and Carl Baker's penalty saw Coventry move to within five points of the play-off zone, as Bournemouth dropped out of the top six.
Matt Tubbs had the Cherries' best chances but saw one effort saved by Joe Murphy, while later slotting just wide after finding himself one-on-one.
Bournemouth keeper Shwan Jalal made several saves but Clarke made it 1-0 with a fine strike into the top corner.
And Baker made sure of the points from the spot after Lewis Grabban handled.
It was Bournemouth's third consecutive defeat and the third match running they have failed to score, as they fell three points off the top two.