Eddie Howe's side wasted plenty of early openings with Matt Tubbs and Lewis Grabban the main culprits and were made to pay when Coventry took the lead just before the break.
Leon Clarke ran on to a long pass out of defence, held off defender Steve Cook and then lashed home his 20th goal of the season from 10 yards.
Clarke was denied another in the 53rd minute by an excellent save from Bournemouth goalkeeper Shwan Jalal before Howe sent on all three substitutes.
Ryan Fraser, Josh McQuoid and Grabban all went close to equalising before Covnetry struck again in the 84th minute.
Grabban was guilty of handling a free-kick and from the subsequent penalty Coventry captain Carl Baker converted easily.
Bournemouth's defeat saw them spiral down to seventh place in the table after they had recently gone top, while Coventry's success kept them in touch with the leading pack.