Cardiff Blues remain in contention for an Amlin Cup quarter-final place despite defeat by already eliminated Exeter Chiefs at the Arms Park.
Lock Don Armand scored the Chiefs' try as they did the double over the Blues in Pool 2.
But Wales winger Alex Cuthbert scored a try for the Blues as they recorded a vital losing bonus point.
The Blues now need results on Sunday to go their way if they are to qualify for the second-tier competition.
The Welsh region needed a three-try win over the Chiefs, who recorded a 44-29 win in the first game between the sides, to guarantee a place in the Amlin Challenge Cup, which they won in 2010.
Northampton have already qualified for a quarter-final spot and the Blues, Edinburgh, Harlequins, Scarlets and Gloucester are in the running for the remaining two places available to sides dropping down from the Heineken Cup.
Exeter, out of Europe and bottom of the group, produced a typically well drilled performance against a young and inexperienced Blues side.
They laid the platform for the win in the first period and even survived going down to 14 men when scrum-half Dave Lewis was yellow carded in the 73rd minute.
Blues full-back Leigh Halfpenny and fly-half Gareth Davies had both missed late penalties when Exeter's Gareth Steenson secured the win with his fourth penalty two minutes from time.
The home side made the worst possible start when they went behind without really touching the ball when Exeter lock Armand was driven over from short range.
Fly-half Steenson added the conversion and two penalties to give the Chiefs a 13-point advantage.
The Blues struggled to get any kind of foothold in the first half with the dominant Chiefs pack dictating proceedings.
The sight of the normally reliable Wales and British and Irish Lions full-back Halfpenny fumbling an easy kick typified the Blues' nervy performance in the first 40 minutes.
But it was Halfpenny who scored the first points for his side with a penalty and he also started the move for the Blues try scored by winger Cuthbert.
Halfpenny launched the attack and Cuthbert and flanker Ellis Jenkins, the Wales Under-20s captain, combined for the Wales and Lions winger to score the under posts.
That made it 13-10 to the Chiefs at the break and after the interval Halfpenny landed his second penalty to draw the Blues level. Steenson replied with his third penalty to put the Chiefs back ahead.
Two further Steenson penalties took the game beyond the hosts to secure a well deserved win for the Chiefs at the end of their campaign.
Cardiff Blues: Leigh Halfpenny; Alex Cuthbert, Gavin Evans, Dafydd Hewitt, Chris Czekaj; Gareth Davies, Lloyd Williams; Sam Hobbs (capt), Kristian Dacey, Benoit Bourrust, Chris Dicomidis, Filo Paulo, Macauley Cook, Robin Copeland, Ellis Jenkins.
Replacements: Marc Breeze, Thomas Davies, Scott Andrews, James Down, Rory Watts-Jones, Lewis Jones, Dan Fish, Richard Smith.
Exeter Chiefs: Luke Arscott; Fetu'u Vainikolo, Sam Hill, Henry Slade, Matt Jess; Gareth Steenson, Dave Lewis; Carl Rimmer, Jack Yeandle, Alex Brown, Dean Mumm (capt), Damian Welch, Dave Ewers, Kai Horstmann, Don Armand.
Replacements: Greg Bateman, Luke Cowan-Dickie, Lloyd Fairbrother, Ben White, James Phillips, Will Chudley, Ceri Sweeney, Jason Shoemark.
Referee: John Lacey (Ireland)