Exeter struck first in the 16th minute with a brilliant team goal.
Richard Logan, Liam Sercombe and Jamie Cureton all combined with some wonderful one-touch passing and from Logan’s smart pass, Cureton curled a lovely shot into the bottom corner from 15 yards.
Bournemouth rarely threatened although Marc Pugh smashed the crossbar with a shot from 20 yards shortly before half-time. All in all it was a disappointing first 45 minutes from the promotion-chasers, who were second best all over the park.
The Cherries started the second half well, but fell further behind when Cureton broke the offside trap and crossed for Logan to score from close range.
Cureton almost made it 3-0, but his rasping drive crashed down off the underside of the crossbar before being cleared, but it was all Exeter as Bournemouth went down with a whimper.