The Ospreys, who are riding high unbeaten in the RaboDirect Pro12 could only muster three Matthew Morgan penalties in the West Country whilst the hosts collected the bonus point with four tries.
The tries for Exeter came from John Andress, Phil Dollman, Josh Tatupu and a penalty try whilst Irish fly-half Gareth Steenson kicked 15-points for his side including three conversions.
The Ospreys, coached by Bridgend’s Steve Tandy for this game, produced a spirited opening with Morgan showing some silky skills from fly half while youngster Eli Walker also looked dangerous when given room to move on the wing.
However the home side had too much experience to eventually claim a bonus point for scoring four tries which could prove crucial at the end of pool play.