THE Ospreys slipped to their first defeat of this season's LV= Cup despite a spirited performance at Exeter.
Morgan Allen touched down for his second try in consecutive matches, while Sam Davies added eight points.
But the Pro12 champions could not repeat the drama of their late victory of Gloucester last week as Exeter held on comfortably after the break.
Exeter fly-half Henry Slade put his team ahead inside two minutes with a penalty.
But it was the Ospreys who controlled the early stages and they grabbed the first try of the night soon after.
Having lost their own line-out ball on the Exeter 22, good work from the Ospreys pack allowed them to win possession back. Exeter scrum-half Junior Poluleuligaga fumbled at the back of the ruck allowing the Ospreys to pounce, with No. 8 Allen touching down to put his team ahead.
Fly-half Davies landed the conversion to give his side a solid platform.
Despite Slade being off target with a penalty, Exeter went back in front when Will Carrick-Smith stretched over the line to score between the posts. Slade converted.
A Davies penalty brought the Ospreys level almost immediately.
But on the stroke of half-time, Exeter snatched the initiative with a try started and finished by full-back Myles Dorrian.
Slade's conversion took the score to 17-10.
Davies, enjoying a fine night with the boot, brought the Ospreys back to within four points with his second penalty of the evening.
But Slade restored the home side's seven-point advantage with a penalty after a period of pressure on the Ospreys line.
Slade slotted another penalty to take the Chiefs ten points clear.
Exeter had to play out the final minutes a couple of players short. No. 8 Dave Ewers was forced off injured after the Chiefs had used all their replacements, then substitute hooker Neil Clark was sent to the sin-bin.
Replacement Matthew Morgan went for the posts with the resulting penalty, looking to secure a bonus point with the final kick of the evening, but was off target.
Ospreys forwards coach Jonathan Humphreys said: "We're generally happy with the progress the younger group is making.
"We've seen plenty of character and, as we'd hoped, we've learned a lot about some individuals.
"It's all part of their development, playing Aviva Premiership teams and playing in front of bigger crowds than they may be used to, and some of the boys have given us plenty to think about as coaches."