Exeter Chiefs missed out on the Premiership play-offs after this defeat and Northampton's win over Worcester.
They led 10-9 at the interval thanks to a Tom Johnson try and five points from the boot of Gareth Steenson.
But four tries in 25 minutes from the home side put the game out of reach.
The Chiefs kept battling though, and scored their customary late tries from Chris Budgen and Matt Jess.
Rob Baxter's side finish another successful season in 5th place, qualifying for next season's Heineken Cup.