Bournemouth completely dominated the first period, with Exeter barely getting out of their own half.
But for all their dominance, they could not score, although Cherries striker Tokelo Rantie came close when he curled a shot against the foot of the post from 18 yards.
Brett Pitman saw two shots blocked by Pat Baldwin and goalkeeper Christy Pym made a superb save from the striker's low drive.
But the deadlock was broken after 54 minutes when Junior Stanislas delivered a low cross which Scot Bennett turned into his own net from close range.
Exeter found themselves 2-0 down after 74 minutes when Stanislas again delivered a good cross from the right, Pym spilled the ball and Brixham-born Dan Gosling marked his full debut and a return to Devon by firing into the roof of the net.
Jimmy Keohane spurned Exeter's best chance, slotting wide from 18 yards with the goal at his mercy.