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The home side got off to a quick start, with Jonny May and Dan Murphy both scoring tries inside the opening 10 minutes to give Gloucester an early lead after Ian Whitten had been sent to the sin bin for a dangerous tackle on Charlie Sharples.
Gareth Steenson kept Exeter in contention, kicking four penalties in the opening 25 minutes to get the visitors back on level terms.
The Chiefs edged ahead just before the break, with a sustained attack resulting in Ben White leaping over following a short burst for the line.
Sione Kalamafoni gave Gloucester some late hope with a third try for the hosts before James Hook added a penalty, leaving them just three points down, but they were unable to complete the comeback.