Adam Stansfield gave Exeter the lead at St James Park when he ran through the Cherries defence and drilled the ball under Shwan Jalal.
However, Exeter failed to make their possession tell and found themselves behind as Bournemouth scored two quickfire goals.
Danny Holland capitalised on Paul James's howler to bring the Cherries level before Brett Pitman ran half the length of the pitch to score a fine individual goal.
Exeter offered little after the break and Pitman capitalised on more shocking defending to grab a third.
Bournemouth could have won by a larger margin, but Pitman saw a shot hit the crossbar from fully 30 yards, while Hollands saw a shot deflected just wide of the Exeter goal.