Cardiff Blues wound up their Heineken Cup campaign in losing fashion at the Arms Park as Exeter claimed a European home and away double over them this season.
Despite coming unstuck, though, the Blues might still have done enough - depending on Sunday's results - to claim a quarter-final place as one of three Heineken qualifiers for the second-tier Amlin Challenge Cup.
Gareth Steenson booted the already-eliminated Chiefs to a 19-13 victory kicking 14 points, including the conversion of lock Dave Armand's early try.
Wales wing Alex Cuthbert touched down for the Blues, with Leigh Halfpenny kicking two penalties and a conversion, and the Welsh side must now wait to see whether or not a losing bonus point will be enough with regard to their Amlin aspirations.
Exeter, firmly out of quarter-final contention following three defeats in five starts, were without captain Dean Mumm due to personal reasons, while England Six Nations squad wing Jack Nowell was rested.
The Blues, meanwhile, went into battle without injured Wales forwards Sam Warburton and Gethin Jenkins as they targeted an immediate recovery from last weekend's comprehensive defeat against Heineken Cup holders Toulon in Nice.
A storming first-half performance by Exeter left the Blues reeling when the sides met in Devon three months ago, and they again made a storming start, racking up 10 points in 13 minutes.
Armand crashed over following relentless pressure to claim a fourth-minute try that skipper Steenson converted, before a 40-metre Steenson penalty left the Blues further adrift.
Steenson extended Exeter's advantage midway through the half, and it would have been even worse for the Blues had their opponents not wasted a couple of threatening positions established by outstanding work from a fired-up Chiefs pack.
Halfpenny opened the Blues' account by booting an angled penalty 10 minutes before the break, although his defensive hesitancy shortly beforehand allowed Exeter an attacking platform that they should have prospered from.
The Blues had been outplayed in terms of territory and possession for much of the first half, yet they prospered from their first genuine attacking opportunity and breached Exeter's defence a minute before the break.
Slick handling by the Blues backs had Exeter back-pedalling in defence and they could do nothing to prevent a try when Cuthbert cut back inside on a superb angle and claimed a high-class score.
Halfpenny converted and the Blues were firmly back in contention, trailing just 13-10.
Cuthbert's score lifted confidence levels in the Blues ranks and they looked a much more cohesive unit during the third quarter in front of a sell-out 12,000 crowd.
The Blues forwards displayed a far healthier appetite for battle than during the opening 20 minutes, and Halfpenny wiped out Exeter's advantage by landing an angled 53rd-minute penalty.
It was an impressive recovery by the Blues, but Steenson soon put Exeter back in front when he completed his penalty hat-trick.
With heavy rain testing the handling skills of both teams, tactical kicking became an inevitable order of the day. Try-scoring opportunities were at a premium, with Halfpenny drifting a long-range penalty wide that would have hauled the Blues level.
The Blues, desperate to keep alive their European hopes in some shape or form this season, established a territorial foothold inside Exeter's 22 as the clock ticked down, and it was a case of keeping their composure after referee John Lacey awarded them an attacking scrum five metres out.
Halfpenny, though, inexplicably missed a 25-metre penalty chance and Exeter breathed a collective sigh of relief before closing the game out through Steenson's clincher.