Edinburgh survived a second-half fightback to become the first Scottish team to win away at the Blues.
Blues (0) 12
Tries: Powell, M Jones
Edinburgh (17) 17
Tries: Lee, Webster
Cons: Laney (2)
A well-worked try for Derrick Lee and Simon Webster's breakaway score helped the visitors to a 17-0 half-time lead.
After a roasting in the interval, the Cardiff side's pack got to grips with the Scots and rolling mauls led to tries for Ryan Powell and Martin Jones.
But the Blues challenge fizzled out, an error-strewn end leaving them likely to miss out on the Heineken Cup next year.
Edinburgh had the better of a lacklustre start to the game and got the reward for their dominance of territory and possession after 20 minutes.
Brendan Laney's pass to Webster in the build-up looked suspiciously forward, but Michael Blair took full advantage of the resultant line break.
The scrum-half got on the outside of the defensive line before feeding Lee, who edged past two despairing tackles for the opening try.
The Blues mounted their first serious attack on 32 minutes, but an attempted Lee Thomas chip through was intercepted by Mike Pyke on the Edinburgh 22.
Laney received the ball in acres of space, pinned his ears back and went for the line.
The labouring centre was caught within metres of the whitewash and his pass inside was knocked on, but the visitors won a penalty which Laney slotted over.
The Blues mounted another attack as half-time approached, but a loose ruck deep in the visitors' half allowed the Scots to pinch possession.
The Blues forwards took the game to Edinburgh after the break
The ball was spun swiftly to Webster, who cantered home from 65 yards for a converted try to make it 17-0 at the break.
The Blues forwards then tore into Edinburgh, winning a kickable penalty that was booted to touch.
A strong rolling maul was held up just short, but scrum-half Powell sniped out of the side and dived under two tackles for the Blues' first score.
The Cardiff side brought on Maama Molitika for his debut, Gareth Williams, and Wales fly-half Nicky Robinson, making his first appearance of the season after a mystery virus.
Edinburgh lock Nathan Hines was then sin-binned for failing to roll away from a tackle.
The resultant penalty was kicked to touch, Molitika claiming the line-out and prop Martin Jones emerging from the maul for a converted try.
But Edinburgh closed things down in the final 20 minutes, and as knock-ons and errors dominated the game slid to a disappointing end.
"We were pleased with the first half and wanted to put them away after the break, but that didn't quite happen," said man-of-the-match Webster.
"It's always tough to win in Wales but we are getting things together in Scotland and I think we're the first Edinburgh team to win in Cardiff.
"It's disappointing we weren't playing like this earlier in the season when we took some beatings, but hopefully we are a better team for it."
A disappointed Blues coach Dai Young said:
"It wasn't good, we have to be honest. We couldn't handle their off-loading in the first half and they blitzed us.
"I told them at half-time that it wasn't acceptable and they were letting themselves down, it was way below our standards of the last six weeks.
"We then showed our character for 20 minutes, but Edinburgh killed it in the end. We just have to put the performance behind us, work harder and get it right."
Blues: N MacLeod; D Dewdney, T Davies, J Bryant, J Vaughton; L Thomas, R Powell; J Yapp, R Thomas, M Jones, D Jones (capt), N Budgett, N Thomas, R Sowden-Taylor, K Schubert.
Replacements: B Evans, G Williams, R Sidoli, M Molitika, N Robinson, N Walne, S James.
Edinburgh: D Lee; M Pyke, M Di Rollo, B Laney, S Webster; P Godman, M Blair; A Jacobsen, D Hall, C Smith, F Pringle, N Hines, T Blackadder (capt), A Strokosch, D Callam.
Replacements: A Kelly, A Dickinson, N Pike, S Cross, R Lawson, P Boston, C Joiner.
Referee: Alan Lewis (Ireland)